Academic literature on the topic 'Topology of real algebraic varieties'

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Journal articles on the topic "Topology of real algebraic varieties"

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Kollár, János. "The topology of Real Algebraic Varieties." Current Developments in Mathematics 2000, no. 1 (2000): 197–231. http://dx.doi.org/10.4310/cdm.2000.v2000.n1.a4.

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Karoubi, Max, and Charles Weibel. "Algebraic and real K-theory of Real varieties." Topology 42, no. 4 (2003): 715–42. http://dx.doi.org/10.1016/s0040-9383(02)00069-1.

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Ozan, Yildiray. "Relative topology of real algebraic varieties in their complexifications." Pacific Journal of Mathematics 217, no. 2 (2004): 291–302. http://dx.doi.org/10.2140/pjm.2004.217.291.

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Laszlo, Yves, and Claude Viterbo. "Estimates of characteristic numbers of real algebraic varieties." Topology 45, no. 2 (2006): 261–80. http://dx.doi.org/10.1016/j.top.2005.08.002.

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Ozan, Yildiray. "On Homotopy Groups of Real Algebraic Varieties and their Complexifications." Geometriae Dedicata 108, no. 1 (2004): 131–40. http://dx.doi.org/10.1007/s10711-004-9648-6.

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Benoist, Olivier, and Olivier Wittenberg. "The tight approximation property." Journal für die reine und angewandte Mathematik (Crelles Journal) 2021, no. 776 (2021): 151–200. http://dx.doi.org/10.1515/crelle-2021-0003.

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Abstract This article introduces and studies the tight approximation property, a property of algebraic varieties defined over the function field of a complex or real curve that refines the weak approximation property (and the known cohomological obstructions to it) by incorporating an approximation condition in the Euclidean topology. We prove that the tight approximation property is a stable birational invariant, is compatible with fibrations, and satisfies descent under torsors of linear algebraic groups. Its validity for a number of rationally connected varieties follows. Some concrete cons
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Kozlov, V. V. "Gyroscopic stabilization of degenerate equilibria and the topology of real algebraic varieties." Doklady Mathematics 77, no. 3 (2008): 412–15. http://dx.doi.org/10.1134/s1064562408030253.

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Viro, O. Ya. "Progress in the topology of real algebraic varieties over the last six years." Russian Mathematical Surveys 41, no. 3 (1986): 55–82. http://dx.doi.org/10.1070/rm1986v041n03abeh003317.

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Geske, Christian. "Algebraic intersection spaces." Journal of Topology and Analysis 12, no. 04 (2019): 1157–94. http://dx.doi.org/10.1142/s1793525319500778.

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We define a variant of intersection space theory that applies to many compact complex and real analytic spaces [Formula: see text], including all complex projective varieties; this is a significant extension to a theory which has so far only been shown to apply to a particular subclass of spaces with smooth singular sets. We verify existence of these so-called algebraic intersection spaces and show that they are the (reduced) chain complexes of known topological intersection spaces in the case that both exist. We next analyze “local duality obstructions,” which we can choose to vanish, and ver
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Soprunova, Evgenia, and Frank Sottile. "Lower Bounds in Real Algebraic Geometry and Orientability of Real Toric Varieties." Discrete & Computational Geometry 50, no. 2 (2013): 509–19. http://dx.doi.org/10.1007/s00454-013-9498-9.

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Dissertations / Theses on the topic "Topology of real algebraic varieties"

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Haydon, James Henri. "Étale homotopy sections of algebraic varieties." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:88019ba2-a589-4179-ad7f-1eea234d284c.

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We define and study the fundamental pro-finite 2-groupoid of varieties X defined over a field k. This is a higher algebraic invariant of a scheme X, analogous to the higher fundamental path 2-groupoids as defined for topological spaces. This invariant is related to previously defined invariants, for example the absolute Galois group of a field, and Grothendieck’s étale fundamental group. The special case of Brauer-Severi varieties is considered, in which case a “sections conjecture” type theorem is proved. It is shown that a Brauer-Severi variety X has a rational point if and only if its étale
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Ozturk, Ali. "Homology Of Real Algebraic Varieties And Morphisms To Spheres." Phd thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/3/12606424/index.pdf.

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abstract HOMOLOGY OF REAL ALGEBRAIC VARIETIES AND MORPHISMS TO SPHERES &uml<br>OZT&uml<br>URK, Ali Ph.D., Department of Mathematics Supervisor: Assoc. Prof. Dr. Yildiray OZAN August 2005, 24 pages Let X and Y be affine nonsingular real algebraic varieties. One of the classical problems in real algebraic geometry is whether a given C1 mapping f : X ! Y can be approximated by regular mappings in the space of C1 mappings. In this thesis, we obtain some sufficient conditions in the case when Y is the standard sphere Sn. In the second part of the thesis, we study mainly the kernel of the induced ma
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Lehmann, Lutz. "Wavelet-Konstruktion als Anwendung der algorithmischen reellen algebraischen Geometrie." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2007. http://dx.doi.org/10.18452/15619.

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Im Rahmen des TERA-Projektes (Turbo Evaluation and Rapid Algorithms) wurde ein neuartiger, hochgradig effizienter probabilistischer Algorithmus zum Lösen polynomialer Gleichungssysteme entwickelt und für den komplexen Fall implementiert. Die Geometrie polarer Varietäten gestattet es, diesen Algorithmus zu einem Verfahren zur Charakterisierung der reellen Lösungsmengen polynomialer Gleichungssysteme zu erweitern. Ziel dieser Arbeit ist es, eine Implementierung dieses Verfahrens zur Bestimmung reeller Lösungen auf eine Klasse von Beispielproblemen anzuwenden. Dabei wurde Wert darauf g
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Santo, Antonio Andrade do Espírito. "Decomposição open book generalizada em conjuntos semi-algébricos." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-06072015-144158/.

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Nos últimos anos, váarios pesquisadores tais como: A. Bodin, A. Dimca, A. Durfee, A. Jacquemard, A. Menegon Neto, A. Némethi, A. Pichon, A. Verjovsky, A. Zaharia, D. Siersma, H. A. Hamm, D. Massey, H. Aguilar-Cabrera, H. H. Vui, J. Cisneros, J. Seade, J. Snoussi, L. D. Tráng, L. Paunescu, L. R. Dias, M. A. S. Ruas, M. Oka, M. Tibar, N. Dutertre, R. N. Araújo dos Santos, S. A. Broughton, T. Gaffney, Y. Chen, entre outros, têm apresentado generalizações dos Teoremas de fibrações de Milnor no ambiente real e complexo (e do Teorema de Kurdyka-Orro-Simon, ver por exemplo [Di, KOS]), visando um melh
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Limoges, Thierry. "Structures produits sur la filtration par le poids des variétés algébriques réelles." Thesis, Nice, 2015. http://www.theses.fr/2015NICE4001/document.

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On associe à chaque variété algébrique définie sur R un complexe de cochaînes filtré, qui calcule la cohomologie à supports compacts et coefficients dans Z_2 de ses points réels. Ce complexe filtré est additif pour les inclusions fermées et acyclique pour la résolution des singularités, et est unique à quasi-isomorphisme filtré près. Il est représenté par la filtration duale de la filtration géométrique sur les chaînes semi-algébriques à supports fermés définie par McCrory and Parusiński, et induit une suite spectrale qui calcule la filtration par le poids sur la cohomologie à supports compact
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"HOMOLOGY OF REAL ALGEBRAIC VARIETIES AND MORPHISMS TO SPHERES." Phd thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/3/12606424/index.pdf.

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Schwerteck, Florian [Verfasser]. "Real algebraic varieties with trivial canonical class and toric geometry / Florian Schwerteck." 2010. http://d-nb.info/1004706243/34.

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"Einstein-Hermitian structures on stable vector bundles." Chinese University of Hong Kong, 1992. http://library.cuhk.edu.hk/record=b5886975.

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by Leung Wai-Man Raymond.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 1992.<br>Includes bibliographical references (leaves [1]-[3] (2nd gp.)).<br>Chapter CHAPTER 0 --- Introduction --- p.1<br>Chapter CHAPTER 1 --- Einstein-Hermitian Vector Bundles<br>Chapter 1.1 --- Preliminaries on Einstein-Hermitian structures --- p.4<br>Chapter 1.2 --- Conformal invariance --- p.7<br>Chapter 1.3 --- A Chern number inequality --- p.9<br>Chapter CHAPTER 2 --- Stable Vector Bundles<br>Chapter 2.1 --- Coherent analytic sheaves --- p.12<br>Chapter 2.2 --- "Torsion-free, reflexive and normal coher
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(8802785), Abhiram Natarajan. "Betti numbers of deterministic and random sets in semi-algebraic and o-minimal geometry." Thesis, 2020.

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<p>Studying properties of random polynomials has marked a shift in algebraic geometry. Instead of worst-case analysis, which often leads to overly pessimistic perspectives, randomness helps perform average-case analysis, and thus obtain a more realistic view. Also, via Erdos' astonishing 'probabilistic method', one can potentially obtain deterministic results by introducing randomness into a question that apriori had nothing to do with randomness. </p> <p><br></p> <p>In this thesis, we study topological questions in real algebraic geometry, o-minimal geometry and random algebraic geometry, wit
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Rahm, Alexander. "Characteristic classes of vector bundles with extra structure." Thesis, 2007. http://hdl.handle.net/11858/00-1735-0000-000D-F285-2.

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Books on the topic "Topology of real algebraic varieties"

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Hironaka, Eriko. Abelian coverings of the complex projective plane branched along configurations of real lines. American Mathematical Society, 1993.

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Real solutions to equations from geometry. American Mathematical Society, 2011.

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Mangolte, Frédéric. Real Algebraic Varieties. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43104-4.

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Cogolludo-Agustín, José Ignacio, and Eriko Hironaka, eds. Topology of Algebraic Varieties and Singularities. American Mathematical Society, 2011. http://dx.doi.org/10.1090/conm/538.

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Akbulut, Selman. Topology of real algebraic sets. Springer-Verlag, 1992.

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Akbulut, Selman, and Henry King. Topology of Real Algebraic Sets. Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4613-9739-7.

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Akbulut, Selman, ed. Real Algebraic Geometry and Topology. American Mathematical Society, 1995. http://dx.doi.org/10.1090/conm/182.

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service), SpringerLink (Online, ed. Questions on Algebraic Varieties. Springer-Verlag Berlin Heidelberg, 2011.

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Conference on Real Algebraic Geometry and Topology (1993 Michigan State University). Real algebraic geometry and topology: A Conference on Real Algebraic Geometry and Topology, December 17-21, 1993, Michigan State University. Edited by Akbulut Selman 1949-. American Mathematical Society, 1995.

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1957-, Gurvits Leonid, and Banff International Research Station for Mathematics Innovation & Discovery, eds. Randomization, relaxation, and complexity in polynomial equation solving: Banff International Research Station Workshop on Randomization, Relaxation, and Complexity, February 28--March 5, 2010, Banff, Ontario [i.e. Alberta], Canada. American Mathematical Society, 2011.

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Book chapters on the topic "Topology of real algebraic varieties"

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Bochnak, Jacek, Michel Coste, and Marie-Françoise Roy. "Topology of Real Algebraic Varieties." In Real Algebraic Geometry. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-03718-8_12.

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Bochnak, Jacek, Michel Coste, and Marie-Françoise Roy. "Real Algebraic Varieties." In Real Algebraic Geometry. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-03718-8_4.

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Haesemeyer, Christian, and Chuck Weibel. "Norm Varieties and the Chain Lemma (After Markus Rost)." In Algebraic Topology. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-01200-6_6.

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Shafarevich, Igor R. "The Topology of Algebraic Varieties." In Basic Algebraic Geometry 2. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-38010-5_3.

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Shafarevich, Igor R. "The Topology of Algebraic Varieties." In Basic Algebraic Geometry 2. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57956-1_3.

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Basu, Saugata, Richard Pollack, and Marie-Francoise Roy. "Elements of Topology." In Algorithms in Real Algebraic Geometry. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-05355-3_7.

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Silhol, Robert. "Preliminaries on real algebraic varieties." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0088816.

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Banaschewski, B. "Stone’s Real Gelfand Duality in Pointfree Topology." In Ordered Algebraic Structures. Springer US, 2002. http://dx.doi.org/10.1007/978-1-4757-3627-4_7.

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Whitney, Hassler. "Elementary Structure of Real Algebraic Varieties." In Hassler Whitney Collected Papers. Birkhäuser Boston, 1992. http://dx.doi.org/10.1007/978-1-4612-2972-8_31.

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Lee, Ronnie, and Steven H. Weintraub. "On certain siegel modular varieties of genus two and levels above two." In Algebraic Topology and Transformation Groups. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0083033.

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Conference papers on the topic "Topology of real algebraic varieties"

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Itenberg, Ilia. "Topology of real algebraic varieties and tropical homology." In The 5th Franco-Japanese-Vietnamese Symposium on Singularities. WORLD SCIENTIFIC, 2020. http://dx.doi.org/10.1142/9789811206030_0002.

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Dufresne, Emilie, Parker Edwards, Heather Harrington, and Jonathan Hauenstein. "Sampling Real Algebraic Varieties for Topological Data Analysis." In 2019 18th IEEE International Conference On Machine Learning And Applications (ICMLA). IEEE, 2019. http://dx.doi.org/10.1109/icmla.2019.00253.

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Wu, Wen-tsun. "On generalized Chern classes and Chern numbers of irreducible complex algebraic varieties with arbitrary singularities." In Geometry and Topology of Manifolds. Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc76-0-12.

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Fortuna, Elisabetta, Patrizia Gianni, Paola Parenti, and Carlo Traverso. "Computing the topology of real algebraic surfaces." In the 2002 international symposium. ACM Press, 2002. http://dx.doi.org/10.1145/780506.780518.

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Seidel, Raimund, and Nicola Wolpert. "On the exact computation of the topology of real algebraic curves." In the twenty-first annual symposium. ACM Press, 2005. http://dx.doi.org/10.1145/1064092.1064111.

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Safey El Din, Mohab, and Éric Schost. "Polar varieties and computation of one point in each connected component of a smooth real algebraic set." In the 2003 international symposium. ACM Press, 2003. http://dx.doi.org/10.1145/860854.860901.

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Serban, Radu, and Edward J. Haug. "Globally Independent Coordinates for Real-Time Vehicle System Simulation." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/dac-5587.

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Abstract Models of the dynamics of multibody systems generally result in a set of differential–algebraic equations (DAE). State–space methods for solving the DAE of motion are based on reduction of the DAE to ordinary differential equations (ODE), by means of local parameterizations of the constraint manifold that must be often modified during a simulation. In this paper it is shown that, for vehicle multibody systems, generalized coordinates that are dual to suspension and/or control forces in the model are independent for the entire range of motion of the system. In addition to the immediate
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