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Дисертації з теми "Geometry, Algebraic"

Автор: Grafiati

Опубліковано: 4 червня 2021

Оновлено: 29 липня 2024

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1

Miscione, Steven. "Loop algebras and algebraic geometry." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=116115.

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This thesis primarily discusses the results of two papers, [Hu] and [HaHu]. The first is an overview of algebraic-geometric techniques for integrable systems in which the AKS theorem is proven. Under certain conditions, this theorem asserts the commutatvity and (potential) non-triviality of the Hamiltonian flow of Ad*-invariant functions once they're restricted to subalgebras. This theorem is applied to the case of coadjoint orbits on loop algebras, identifying the flow with a spectral curve and a line bundle via the Lax equation. These results play an important role in the discussion of [HaHu

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2

Lurie, Jacob 1977. "Derived algebraic geometry." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/30144.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.<br>Includes bibliographical references (p. 191-193).<br>The purpose of this document is to establish the foundations for a theory of derived algebraic geometry based upon simplicial commutative rings. We define derived versions of schemes, algebraic spaces, and algebraic stacks. Our main result is a derived analogue of Artin's representability theorem, which provides a precise criteria for the representability of a moduli functor by geometric objects of these types.<br>by Jacob Lurie.<br>Ph.D.

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3

Balchin, Scott Lewis. "Augmented homotopical algebraic geometry." Thesis, University of Leicester, 2017. http://hdl.handle.net/2381/40623.

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Анотація:

In this thesis we are interested in extending the theory of homotopical algebraic geometry, which itself is a homotopification of classical algebraic geometry. We introduce the concept of augmentation categories, which are a class of generalised Reedy categories. An augmentation category is a category which has enough structure that we can mirror the simplicial constructions which make up the theory of homotopical algebraic geometry. In particular, we construct a Quillen model structure on their presheaf categories, and introduce the concept of augmented hypercovers to define a local model str

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4

Rennie, Adam Charles. "Noncommutative spin geometry." Title page, contents and introduction only, 2001. http://web4.library.adelaide.edu.au/theses/09PH/09phr4163.pdf.

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5

Dos, Santos João Pedro Pinto. "Fundamental groups in algebraic geometry." Thesis, University of Cambridge, 2006. https://www.repository.cam.ac.uk/handle/1810/252015.

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6

Slaatsveen, Anna Aarstrand. "Decoding of Algebraic Geometry Codes." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for fysikk, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-13729.

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Анотація:

Codes derived from algebraic curves are called algebraic geometry (AG) codes. They provide a way to correct errors which occur during transmission of information. This paper will concentrate on the decoding of algebraic geometry codes, in other words, how to find errors. We begin with a brief overview of some classical result in algebra as well as the definition of algebraic geometry codes. Then the theory of cyclic codes and BCH codes will be presented. We discuss the problem of finding the shortest linear feedback shift register (LFSR) which generates a given finite sequence. A decoding algo

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7

Birkar, Caucher. "Topics in modern algebraic geometry." Thesis, University of Nottingham, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.421475.

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8

Lundman, Anders. "Topics in Combinatorial Algebraic Geometry." Doctoral thesis, KTH, Matematik (Avd.), 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-176878.

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Анотація:

This thesis consists of six papers in algebraic geometry –all of which have close connections to combinatorics. In Paper A we consider complete smooth toric embeddings X ↪ P^N such that for a fixed positive integer k the t-th osculating space at every point has maximal dimension if and only if t ≤ k. Our main result is that this assumption is equivalent to that X ↪ P^N is associated to a Cayley polytope of order k having every edge of length at least k. This result generalizes an earlier characterisation by David Perkinson. In addition we prove that the above assumptions are equivalent to requ

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9

Hu, Jiawei. "Partial actions in algebraic geometry." Doctoral thesis, Universite Libre de Bruxelles, 2018. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/273459.

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Анотація:

We introduce geometrically partial comodules over coalgebras in monoidal categories, as an alternative notion to the notion of partial action and coaction of Hopf algebras introduced by Caenepeel and Janssen. We show that our new notion suits better if one wants to describe phenomena of partial actions in algebraic geometry. We show that under mild conditions, the category of geometric partial comodules is complete and cocomplete and the category of partial comodules over a Hopf algebra is lax monoidal. We develop a Hopf-Galois theory for geometric partial coactions to illustrate that our new

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10

Garcia-Puente, Luis David. "Algebraic Geometry of Bayesian Networks." Diss., Virginia Tech, 2004. http://hdl.handle.net/10919/11133.

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Анотація:

We develop the necessary theory in algebraic geometry to place Bayesian networks into the realm of algebraic statistics. This allows us to create an algebraic geometry--statistics dictionary. In particular, we study the algebraic varieties defined by the conditional independence statements of Bayesian networks. A complete algebraic classification, in terms of primary decomposition of polynomial ideals, is given for Bayesian networks on at most five random variables. Hidden variables are related to the geometry of higher secant varieties. Moreover, a complete algebraic classification, in ter

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11

Mikami, Ryota. "Tropical geometry and algebraic cycles." Doctoral thesis, Kyoto University, 2021. http://hdl.handle.net/2433/263437.

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12

Kileel, Joseph David. "Algebraic Geometry for Computer Vision." Thesis, University of California, Berkeley, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10282753.

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Анотація:

<p> This thesis uses tools from algebraic geometry to solve problems about three-dimensional scene reconstruction. 3D reconstruction is a fundamental task in multiview geometry, a field of computer vision. Given images of a world scene, taken by cameras in unknown positions, how can we best build a 3D model for the scene? Novel results are obtained for various challenging minimal problems, which are important algorithmic routines in Random Sampling Consensus pipelines for reconstruction. These routines reduce overfitting when outliers are present in image data. </p><p> Our approach thro

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13

Waelder, Robert. "Elliptic genera in algebraic geometry." Diss., Restricted to subscribing institutions, 2008. http://proquest.umi.com/pqdweb?did=1619148881&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD.

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14

Milione, Piermarco. "Shimura curves and their p-adic uniformization = Corbes de Shimura i les seves uniformitzacions p-àdiques." Doctoral thesis, Universitat de Barcelona, 2016. http://hdl.handle.net/10803/402209.

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Анотація:

The main purpose of this dissertation is to introduce Shimura curves from the non-Archimedean point of view, paying special attention to those aspects that can make this theory amenable for computations. Despite the fact that the theory of p-adic uniformization of Shimura curves goes back to the 1960s with the results of Cerednik and Drinfeld, only in the last years explicit examples related to these uniformizations have been computed. The structure of this dissertation is as follows. In Chapter 1 we introduce Shimura curves starting from an indefinite quaternion algebra H over a totally re

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15

Eklund, David. "Topics in computation, numerical methods and algebraic geometry." Doctoral thesis, KTH, Matematik (Avd.), 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-25941.

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This thesis concerns computation and algebraic geometry. On the computational side we have focused on numerical homotopy methods. These procedures may be used to numerically solve systems of polynomial equations. The thesis contains four papers. In Paper I and Paper II we apply continuation techniques, as well as symbolic algorithms, to formulate methods to compute Chern classes of smooth algebraic varieties. More specifically, in Paper I we give an algorithm to compute the degrees of the Chern classes of smooth projective varieties and in Paper II we extend these ideas to cover also the degre

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16

Björklund, Johan. "Knots and Surfaces in Real Algebraic and Contact Geometry." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-156908.

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This thesis consists of a summary and three articles. The thesis is devoted to the study of knots and surfaces with additional geometric structures compared to the classical smooth structure. In Paper I, real algebraic rational knots in real projective space are studied up to rigid isotopy and we show that two real rational algebraic knots of degree at most 5 are rigidly isotopic if, and only if, their degree and encomplexed writhe are equal. We also show that any smooth irreducible knot which admits a plane projection with less than or equal to four crossings has a rational parametrization of

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17

Heier, Gordon. "Some effective results in algebraic geometry." [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=965086631.

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18

De, Zeeuw Frank. "An algebraic view of discrete geometry." Thesis, University of British Columbia, 2011. http://hdl.handle.net/2429/38158.

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Анотація:

This thesis includes three papers and one expository chapter as background for one of the papers. These papers have in common that they combine algebra with discrete geometry, mostly by using algebraic tools to prove statements from discrete geometry. Algebraic curves and number theory also recur throughout the proofs and results. In Chapter 1, we will detail these common threads. In Chapter 2, we prove that an infinite set of points in R² such that all pairwise distances are rational cannot be contained in an algebraic curve, except if that curve is a line or a circle, in which case at most 4

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19

Thaddeus, Michael. "Algebraic geometry and the Verlinde formula." Thesis, University of Oxford, 1992. http://ora.ox.ac.uk/objects/uuid:12af7dda-26f7-44ec-b335-74193ce1c538.

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20

Francis, John (John Nathan Kirkpatrick). "Derived algebraic geometry over En̳-rings." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/43792.

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Анотація:

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.<br>In title on t.p., double underscored "n" appears as subscript.<br>Includes bibliographical references (p. 55-56).<br>We develop a theory of less commutative algebraic geometry where the role of commutative rings is assumed by En-rings, that is, rings with multiplication parametrized by configuration spaces of points in Rn. As n increases, these theories converge to the derived algebraic geometry of Tobn-Vezzosi and Lurie. The class of spaces obtained by gluing En-rings form a geometric counterpart to En-cate

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21

Kotschick, Dieter. "On the geometry of certain 4 - manifolds." Thesis, University of Oxford, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.236179.

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22

Li, Shiyue. "Tropical Derivation of Cohomology Ring of Heavy/Light Hassett Spaces." Scholarship @ Claremont, 2017. http://scholarship.claremont.edu/hmc_theses/104.

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Анотація:

The cohomology of moduli spaces of curves has been extensively studied in classical algebraic geometry. The emergent field of tropical geometry gives new views and combinatorial tools for treating these classical problems. In particular, we study the cohomology of heavy/light Hassett spaces, moduli spaces of heavy/light weighted stable curves, denoted as $\calm_{g, w}$ for a particular genus $g$ and a weight vector $w \in (0, 1]^n$ using tropical geometry. We survey and build on the work of \citet{Cavalieri2014}, which proved that tropical compactification is a \textit{wonderful} compactificat

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23

Lundkvist, Christian. "Moduli spaces of zero-dimensional geometric objects." Doctoral thesis, Stockholm : Matematik, Kungliga Tekniska högskolan, 2009. http://www.diva-portal.org/smash/record.jsf?searchId=1&pid=diva2:223079.

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24

Sarmiento-Lopez, X. I. "Algebraic problems in matroid theory." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.298554.

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25

Lewis, Matthew. "Error correction of generalised algebraic-geometry codes." Thesis, Imperial College London, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.407473.

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26

Zong, Hong R. "Topics in birational geometry of algebraic varieties." Thesis, Princeton University, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3665359.

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<p> Various questions related to birational properties of algebraic varieties are concerned. </p><p> Rationally connected varieties are recognized as the buildings blocks of all varieties by the Minimal Model theory. We prove that every curve on a separably rationally connected variety is rationally equivalent to a (non-effective) integral sum of rational curves. That is, the Chow group of 1-cycles is generated by rational curves. As a consequence, we solve a question of Professor Burt Totaro on integral Hodge classes on rationally connected 3-folds. And by a result of Professor Claire Vois

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27

Shifler, Ryan M. "Computational Algebraic Geometry Applied to Invariant Theory." Thesis, Virginia Tech, 2013. http://hdl.handle.net/10919/23154.

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Commutative algebra finds its roots in invariant theory and the connection is drawn from a modern standpoint. The Hilbert Basis Theorem and the Nullstellenstatz were considered lemmas for classical invariant theory. The Groebner basis is a modern tool used and is implemented with the computer algebra system Mathematica. Number 14 of Hilbert\'s 23 problems is discussed along with the notion of invariance under a group action of GLn(C). Computational difficulties are also discussed in reference to Groebner bases and Invariant theory.The straitening law is presented from a Groebner basis point of

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28

Massarenti, Alex. "Biregular and Birational Geometry of Algebraic Varieties." Doctoral thesis, SISSA, 2013. http://hdl.handle.net/20.500.11767/4679.

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Анотація:

Every area of mathematics is characterized by a guiding problem. In algebraic geometry such problem is the classification of algebraic varieties. In its strongest form it means to classify varieties up to biregular morphisms. However, birationally equivalent varieties share many interesting properties. Therefore for any birational equivalence class it is natural to work out a variety, which is the simplest in a suitable sense, and then study these varieties. This is the aim of birational geometry. In the first part of this thesis we deal with the biregular geometry of moduli spaces of curves,

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29

Redman, Lynn. "Algebraic Methods for Proving Geometric Theorems." CSUSB ScholarWorks, 2019. https://scholarworks.lib.csusb.edu/etd/923.

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Algebraic geometry is the study of systems of polynomial equations in one or more variables. Thinking of polynomials as functions reveals a close connection between affine varieties, which are geometric structures, and ideals, which are algebraic objects. An affine variety is a collection of tuples that represents the solutions to a system of equations. An ideal is a special subset of a ring and is what provides the tools to prove geometric theorems algebraically. In this thesis, we establish that a variety depends on the ideal generated by its defining equations. The ability to change the b

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30

Hammes, Emily. "Unifications of Pythagorean Triple Schema." Digital Commons @ East Tennessee State University, 2019. https://dc.etsu.edu/honors/502.

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Euclid’s Method of finding Pythagorean triples is a commonly accepted and applied technique. This study focuses on a myriad of other methods behind finding such Pythagorean triples. Specifically, we discover whether or not other ways of finding triples are special cases of Euclid’s Method.

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31

Miadantsoa, Rakoto. "Groupes finis d'automorphismes des varietes abeliennes de dimension deux." Toulouse 3, 1988. http://www.theses.fr/1988TOU30051.

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On etablit dans un premier chapitre la liste des sous-groupes finis g dits effectifs, contenus dans sl(2, c), qui peuvent apparaitre comme sous-groupes finis d'automorphismes d'une surface abelienne. Les deuxieme et troisieme chapitres sont consacres a la description et classification des g-surfaces: ce sont les surfaces abeliennes polarisees associees a g, dont la polarisation est g-invariante. Le cas ou g est contenu dans gl(2, c) est examine dans le dernier chapitre

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32

MOUSSA, OUSMANE. "Theoremes des zeros centraux en geometrie analytique reelle." Rennes 1, 1989. http://www.theses.fr/1989REN10062.

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On etudie dans ce travail les theoremes des zeros centraux de la geometrie analytique reelle: il s'agit de degager une caracterisation algebrique des ideaux de fonctions analytiques s'annulant sur un ensemble de points contenus dans la partie de dimension maximale (c'est-a-dire les points centraux) d'un ensemble (ou d'un germe d'ensemble) analytique reel. Ce probleme est traite dans le cas local, puis dans le cas relatif aux ensembles c-analytiques compacts. La methode de demonstration, dans les deux cas, utilise la theorie du spectre reel pour construire une bonne correspondance - l'operation

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33

Le, Stum Bernard. "Cohomologie rigide et varietes abeliennes." Rennes 1, 1985. http://www.theses.fr/1985REN10007.

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On decrit la cohomologie de de rham d'une variete abelienne a reduction semi-stable sur un corps local (de caracteristique 0) a l'aide d'une theorie cohomologique recente : la cohomologie rigide des varietes de caracteristique p0. Comme grothendieck l'avait montre pour le module de tate, le premier espace de cohomologie de de rham d'une telle variete abelienne est naturellement muni d'une structure d'extension panachee. Cette extension panachee est construite autour du premier espace de cohomologie rigide de la fibre speciale du modele de neron, lequel est naturellement muni d'une structure de

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34

Jadda, Zoubida. "Constructions de places reelles et geometrie semi-algebrique." Rennes 1, 1986. http://www.theses.fr/1986REN10102.

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Cette these a pour objet de montrer l'existence d'une chaine d'anneaux de valuations reels d'un corps de fonctions r(v) d'une variete algebrique affine irreductible v, qui sont convexes pour un meme ordre sur r(v) et dont le centre, la dimension, le rang et le rang rationnel, verifiant certaines conditions, sont donnes. La technique de demonstration est un pur produit de la geometrie algebrique reelle. Elle utilise le spectre et la triangulation par un homeomorphisme semi-algebrique

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35

Fekak, Azzeddine. "Sur les exposants de Lojasiewicz." Grenoble 2 : ANRT, 1986. http://catalogue.bnf.fr/ark:/12148/cb37597565q.

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36

Deshpande, D. V. "Topological methods in algebraic geometry : cohomology rings, algebraic cobordism and higher Chow groups." Thesis, University of Cambridge, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.598515.

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This thesis is divided into three chapters. The first chapter is about the cohomology ring of the space of rotational functions. In the second chapter, we define algebraic cobordism of classifying spaces, Ω*(<i>BG</i>) and <i>G</i>-equivariant algebraic cobordism Ω*<i><sub>G</sub></i>(-) for a linear algebraic group <i>G. </i>We prove some properties of the coniveau filtration on algebraic cobordism, denoted <i>F<sup>j</sup></i>(Ω*(-)); which are required for the definition to work. We show that <i>G</i>-equivariant cobordism satisfies the localization exact sequence. We compute Ω*(<i>BG</i>)

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37

Gong, Shengjun, and 龔勝軍. "Linear coordinates, test elements, retracts and automorphic orbits." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B40988065.

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38

Gong, Shengjun. "Linear coordinates, test elements, retracts and automorphic orbits." Click to view the E-thesis via HKUTO, 2008. http://sunzi.lib.hku.hk/hkuto/record/B40988065.

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39

Nyman, Adam. "The geometry of points on quantum projectivizations /." Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/5727.

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40

Abbott, Kevin Toney. "Applications of algebraic geometry to object/image recognition." [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-1935.

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41

Dindyal, Jaguthsing Presmeg Norma C. "Algebraic thinking in geometry at high school level." Normal, Ill. Illinois State University, 2003. http://wwwlib.umi.com/cr/ilstu/fullcit?p3087865.

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Анотація:

Thesis (Ph. D.)--Illinois State University, 2003.<br>Title from title page screen, viewed November 15, 2005. Dissertation Committee: Norma C. Presmeg (chair), Nerida F. Ellerton, Beverly S. Rich, Sharon S. McCrone. Includes bibliographical references (leaves 208-219) and abstract. Also available in print.

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42

Hampton, III Earl Ravi M. "A PRIMER FOR THE FOUNDATIONS OF ALGEBRAIC GEOMETRY." [Greenville, N.C.] : East Carolina University, 2010. http://hdl.handle.net/10342/2797.

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43

Tang, Xin. "Applications of noncommutative algebraic geometry to representation theory /." Search for this dissertation online, 2006. http://wwwlib.umi.com/cr/ksu/main.

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44

Jost, Christine. "Topics in Computational Algebraic Geometry and Deformation Quantization." Doctoral thesis, Stockholms universitet, Matematiska institutionen, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-87399.

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Анотація:

This thesis consists of two parts, a first part on computations in algebraic geometry, and a second part on deformation quantization. More specifically, it is a collection of four papers. In the papers I, II and III, we present algorithms and an implementation for the computation of degrees of characteristic classes in algebraic geometry. Paper IV is a contribution to the field of deformation quantization and actions of the Grothendieck-Teichmüller group. In Paper I, we present an algorithm for the computation of degrees of Segre classes of closed subschemes of complex projective space. The al

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45

Riccomagno, Eva M. "Algebraic geometry in experimental design and related fields." Thesis, University of Warwick, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.263314.

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46

Di, Natale Carmelo. "Grassmannians and period mappings in derived algebraic geometry." Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.709191.

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47

Anderson, William Erik 1976. "Applications of algebraic geometry to coding & cryptography." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/86656.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.<br>Includes bibliographical references (p. 73-74).<br>by William Erik Anderson.<br>S.M.

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48

Abou-Rached, John. "Sheaves and schemes: an introduction to algebraic geometry." Kansas State University, 2016. http://hdl.handle.net/2097/32608.

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Master of Science<br>Department of Mathematics<br>Roman Fedorov<br>The purpose of this report is to serve as an introduction to the language of sheaves and schemes via algebraic geometry. The main objective is to use examples from algebraic geometry to motivate the utility of the perspective from sheaf and scheme theory. Basic facts and definitions will be provided, and a categorical approach will be frequently incorporated when appropriate.

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49

Berardini, Elena. "Algebraic geometry codes from surfaces over finite fields." Thesis, Aix-Marseille, 2020. http://www.theses.fr/2020AIXM0170.

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Nous proposons, dans cette thèse, une étude théorique des codes géométriques algébriques construits à partir de surfaces définies sur les corps finis. Nous prouvons des bornes inférieures pour la distance minimale des codes sur des surfaces dont le diviseur canonique est soit nef soit anti-strictement nef et sur des surfaces sans courbes irréductibles de petit genre. Nous améliorons ces bornes inférieures dans le cas des surfaces dont le nombre de Picard arithmétique est égal à un, des surfaces sans courbes de petite auto-intersection et des surfaces fibrées. Ensuite, nous appliquons ces borne

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50

Drake, Nathan. "Decoding of multipoint algebraic geometry codes via lists." Connect to this title online, 2009. http://etd.lib.clemson.edu/documents/1263409538/.

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