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Relevant bibliographies by topics / Curve genus

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Academic literature on the topic 'Curve genus'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Curve genus"

1

Mourao, Michael. "Extending Elliptic Curve Chabauty to higher genus curves." Manuscripta Mathematica 143, no. 3-4 (2013): 355–77. http://dx.doi.org/10.1007/s00229-013-0621-2.

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Cossidente, A., G. Korchmáros, and F. Torres. "Curves of large genus covered by the hermitian curve." Communications in Algebra 28, no. 10 (2000): 4707–28. http://dx.doi.org/10.1080/00927870008827115.

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Bröker, Reinier, Everett W. Howe, Kristin E. Lauter, and Peter Stevenhagen. "Genus-2 curves and Jacobians with a given number of points." LMS Journal of Computation and Mathematics 18, no. 1 (2015): 170–97. http://dx.doi.org/10.1112/s1461157014000461.

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AbstractWe study the problem of efficiently constructing a curve $C$ of genus $2$ over a finite field $\mathbb{F}$ for which either the curve $C$ itself or its Jacobian has a prescribed number $N$ of $\mathbb{F}$-rational points.In the case of the Jacobian, we show that any ‘CM-construction’ to produce the required genus-$2$ curves necessarily takes time exponential in the size of its input.On the other hand, we provide an algorithm for producing a genus-$2$ curve with a given number of points that, heuristically, takes polynomial time for most input values. We illustrate the practical applica

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Baba, Srinath, and Håkan Granath. "Genus 2 Curves with Quaternionic Multiplication." Canadian Journal of Mathematics 60, no. 4 (2008): 734–57. http://dx.doi.org/10.4153/cjm-2008-033-7.

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AbstractWe explicitly construct the canonical rational models of Shimura curves, both analytically in terms of modular forms and algebraically in terms of coefficients of genus 2 curves, in the cases of quaternion algebras of discriminant 6 and 10. This emulates the classical construction in the elliptic curve case. We also give families of genus 2 QMcurves, whose Jacobians are the corresponding abelian surfaces on the Shimura curve, and with coefficients that are modular forms of weight 12. We apply these results to show that our j-functions are supported exactly at those primes where the gen

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Bruin, Nils. "The arithmetic of Prym varieties in genus 3." Compositio Mathematica 144, no. 2 (2008): 317–38. http://dx.doi.org/10.1112/s0010437x07003314.

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AbstractGiven a curve of genus 3 with an unramified double cover, we give an explicit description of the associated Prym variety. We also describe how an unramified double cover of a non-hyperelliptic genus 3 curve can be mapped into the Jacobian of a curve of genus 2 over its field of definition and how this can be used to perform Chabauty- and Brauer–Manin-type calculations for curves of genus 5 with an fixed-point-free involution. As an application, we determine the rational points on a smooth plane quartic and give examples of curves of genus 3 and 5 violating the Hasse principle. The meth

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Fan, Jing, Xuejun Fan, Ningning Song, and Long Wang. "Hyperelliptic Covers of Different Degree for Elliptic Curves." Mathematical Problems in Engineering 2022 (July 4, 2022): 1–11. http://dx.doi.org/10.1155/2022/9833393.

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In elliptic curve cryptography (ECC) and hyperelliptic curve cryptography (HECC), the size of cipher-text space defined by the cardinality of Jacobian is a significant factor to measure the security level. Counting problems on Jacobians of elliptic curve can be solved in polynomial time by Schoof–Elkies–Atkin (SEA) algorithm. However, counting problems on Jacobians of hyperelliptic curves are solved less satisfactorily than those on elliptic curves. So, we consider the construction of the cover map from the hyperelliptic curves to the elliptic curves to convert point counting problems on hyper

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Moreno-Mejía, Israel. "A Canonical Curve of Genus 17." Results in Mathematics 66, no. 1-2 (2014): 65–86. http://dx.doi.org/10.1007/s00025-014-0364-8.

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Balakrishnan, Jennifer S., Netan Dogra, J. Steffen Müller, Jan Tuitman, and Jan Vonk. "Quadratic Chabauty for modular curves: algorithms and examples." Compositio Mathematica 159, no. 6 (2023): 1111–52. http://dx.doi.org/10.1112/s0010437x23007170.

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We describe how the quadratic Chabauty method may be applied to determine the set of rational points on modular curves of genus $g>1$ whose Jacobians have Mordell–Weil rank $g$ . This extends our previous work on the split Cartan curve of level 13 and allows us to consider modular curves that may have few known rational points or non-trivial local height contributions at primes of bad reduction. We illustrate our algorithms with a number of examples where we determine the set of rational points on several modular curves of genus 2 and 3: this includes Atkin–Lehner quotients $X_0^+(N)$ of pr

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Pál, Ambrus. "Solvable Points on Projective Algebraic Curves." Canadian Journal of Mathematics 56, no. 3 (2004): 612–37. http://dx.doi.org/10.4153/cjm-2004-028-0.

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AbstractWe examine the problem of finding rational points defined over solvable extensions on algebraic curves defined over general fields. We construct non-singular, geometrically irreducible projective curves without solvable points of genus g, when g is at least 40, over fields of arbitrary characteristic. We prove that every smooth, geometrically irreducible projective curve of genus 0, 2, 3 or 4 defined over any field has a solvable point. Finally we prove that every genus 1 curve defined over a local field of characteristic zero with residue field of characteristic p has a divisor of deg

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Sáez, Meritxell. "Classification of degree two curves in the symmetric square with positive self-intersection." Advances in Geometry 18, no. 2 (2018): 161–80. http://dx.doi.org/10.1515/advgeom-2017-0046.

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Abstract We give a precise classification of the pairs (C, B͠) with C a smooth curve of genus g and B͠ ⊂ C(2) a curve of degree two and positive self-intersection. We prove that there are no such pairs if g < pa(B͠) < 2g−1. We study the singularities and self-intersection of any degree two curve in C(2). Moreover, we give examples of curves with arithmetic genus in the Brill–Noether range and positive self-intersection on C × C.

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Dissertations / Theses on the topic "Curve genus"

1

Flynn, Eugene Victor. "Curves of genus 2." Thesis, University of Cambridge, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.305382.

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Balamohan, Balasingham. "Accelerating the scalar multiplication on genus 2 hyperelliptic curve cryptosystems." Thesis, University of Ottawa (Canada), 2010. http://hdl.handle.net/10393/28379.

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Elliptic Curve Cryptography (ECC) was independently introduced by Koblitz and Miller in the eighties. ECC requires shorter sizes of underlying finite fields in comparison to other public key cryptosystems such as RSA, introduced by Rivest, Shamir and Adleman. Hyperelliptic curves, a generalization of elliptic curves, require decreasing field size as genus increases. Hyperelliptic curves of genus g achieve equivalent security of ECC with field size 1/g times the size of field of ECC for g ≤ 4. Recently, a lot of research is being focused on increasing the efficiency of hyperelliptic curve c

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Perlis, Alexander R. "The projective geometry of curves of genus one, and an algorithm for the Jacobian of such a curve." Diss., The University of Arizona, 2004. http://hdl.handle.net/10150/280640.

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Given equations with k-rational coefficients that define a curve C of genus 1 over a perfect field k, can we find equations that define its jacobian J(C)? The problem is trivial when the degree n of a k-rational divisor on C is equal to 1. For the cases 2 ≤ n ≤ 4, certain standard forms for C appear classically, and the classical invariant theory of those forms turns out to contain equations that define J(C). This modern interpretation of classical results was explained for n = 2 in 1954, for n = 3 in 2001, and for n = 4 in 1996. A standard form for C and its invariant theory was worked out

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Bousseau, Pierrick. "Quantum mirrors of log Calabi-Yau surfaces and higher genus curve counting." Thesis, Imperial College London, 2018. http://hdl.handle.net/10044/1/63815.

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We present three results, at the intersection of tropical geometry, enumerative geometry, mirror symmetry and non-commutative algebra. 1. A correspondence between Block-Göttsche q-refined tropical curve counting and higher genus log Gromov-Witten theory of toric surfaces. 2. A correspondence between q-refined two-dimensional Kontsevich-Soibelman scattering diagrams and higher genus log Gromov-Witten theory of log Calabi-Yau surfaces. 3. A q-deformation of the Gross-Hacking-Keel mirror construction, producing a deformation quantization with canonical basis for the Gross-Hacking-Keel families o

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RIGATO, ALESSANDRA. "Uniqueness of optimal curves over F2 of small genus." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2009. http://hdl.handle.net/2108/1073.

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Una curva ottimale su Fq è definita come una curva proiettiva, liscia e assolutamente irriducibile definita sul campo finito Fq che ha il massimo numero di punti Fq-razionali consentito per il suo genere. I primi esempi di crve ottimali definite su F2 risalgono agli anni ottanta e sono dovuti a J.-P.Serre: applicando tecniche di teoria del corpo delle classi, Serre costruisce queste curve come ricoprimenti abeliani della retta proiettiva o di una curva ellittica di equazione data definita su F2. Dimostriamo in questa tesi che una curva ottimale di genere g definita su F2 è unica a meno di F2-m

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Kuchtová, Ludmila. "Růstové charakteristiky termofilních mikroorganismů." Master's thesis, Vysoké učení technické v Brně. Fakulta chemická, 2010. http://www.nusl.cz/ntk/nusl-216667.

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The aim of this work was focused on study of influence of cultivation conditions on growth of thermophilic bacteria Thermus aquaticus, Thermus scotoductus, Geobacillus thermodenitrificans and Geobacillus thermocatenulatus in cultivation medium recommended by Czech Collection of Microorganisms (CCM). The change of concentration of biomass during cultivation with various pH of media, cultivation temperature, agitation rate and with addition of glucose to medium during cultivation in Erlenmayer flasks was observed. Results served for determination of optimal growth conditions for each microorgani

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Borowka, Pawel. "Non-simple abelian varieties and (1,3) Theta divisors." Thesis, University of Bath, 2012. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.564009.

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This thesis studies non-simple Jacobians and non-simple abelian varieties. The moti- vation of the study is a construction which gives a distinguished genus 4 curve in the linear system of a (1, 3)-polarised surface. The main theorem characterises such curves as hyperelliptic genus 4 curves whose Jacobian contains a (1, 3)-polarised surface. This leads to investigating the locus of non-simple principally polarised abelian g- folds. The main theorem of this part shows that the irreducible components of this locus are Is~, defined as the locus of principally polarised g-folds having an abelian s

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Zito, Giuseppe. "Arf good semigroups." Doctoral thesis, Università di Catania, 2019. http://hdl.handle.net/10761/4113.

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In this thesis we explore the properties of the Arf good subsemigroups of N^r, with r>1. We give a way to compute all the Arf semigroups with a given collection of multiplicity branches. We also deal with the problem of determining the Arf closure of a set of vectors and of a good semigroup, extending the concept of characters of an Arf numerical semigroup to Arf good semigroups. Furthermore we present some procedures to calculate the set of the Arf good semigroups with a given conductor and with a given genus. Finally we give an effcient algorithm for the computation of the Arf Closure of

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9

Sadek, Mohammad. "Models of genus one curves." Thesis, University of Cambridge, 2010. https://www.repository.cam.ac.uk/handle/1810/225136.

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In this thesis we give insight into the minimisation problem of genus one curves defined by equations other than Weierstrass equations. We are interested in genus one curves given as double covers of P1, plane cubics, or complete intersections of two quadrics in P3. By minimising such a curve we mean making the invariants associated to its defining equations as small as possible using a suitable change of coordinates. Westudy the non-uniqueness of minimisations of the genus one curves described above. To achieve this goal we investigate models of genus one curves over Henselian discretevaluati

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10

TORRE, OSCAR ALFREDO PAZ LA. "GENUS THREE CURVES IN CHARACTERISTIC TWO." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2003. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=4303@1.

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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>Estudamos a variedade M3 de curvas de gênero três em característica dois. Para cada uma destas curvas calculamos seus possíveis números de pontos de Weierstrass, seus pesos, normalizações de muitos loci no espaço de moduli, entre outras coisas. Tratamos ainda do conceito de ponto de Galois.<br>We study the variety M3 of curves of genus three in characteristic two. For each of the curves we compute the possible number of Weierstrass points, their weights, normalizations of many loci in the moduli space, and so on. We also de

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Books on the topic "Curve genus"

1

Schmidt, Martin U. Integrable systems and Riemann surfaces of infinite genus. American Mathematical Society, 1996.

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2

Ishizaka, Mizuho. Monodromies of hyperelliptic families of genus three curves. Tohoku University, 2001.

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3

Xue, Hang. The arithmetic and geometry of genus four curves. [publisher not identified], 2014.

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Malmendier, Andreas, and Tony Shaska, eds. Higher Genus Curves in Mathematical Physics and Arithmetic Geometry. American Mathematical Society, 2018. http://dx.doi.org/10.1090/conm/703.

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5

Bernie, Devlin, ed. Intelligence, genes, and success: Scientists respond to The bell curve. Springer, 1997.

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6

V, Flynn E., ed. Prolegomena to a middlebrow arithmetic of curves of genus 2. Cambridge University Press, 1996.

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7

Dr, Fitzgerald Michael, ed. Asperger syndrome: A gift or a curse? Nova Science Publishers, 2005.

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8

Cassels, J. W. S., and E. V. Flynn. Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2. Cambridge University Press, 2010.

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9

Hall, Adam C. Divine Genius: The Unlearning Curve. Waterside Press, 2021.

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10

Thompson, Mary E. His Curvy Genius. BluEyed Press, 2022.

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Book chapters on the topic "Curve genus"

1

Boston, N., T. Clancy, Y. Liow, and J. Webster. "Genus Two Hyperelliptic Curve Coprocessor." In Cryptographic Hardware and Embedded Systems - CHES 2002. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/3-540-36400-5_29.

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Orzech, Grace, and Morris Orzech. "The Genus of a Singular Curve." In Plane Algebraic Curves. CRC Press, 2024. https://doi.org/10.1201/9781003573517-16.

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Edwards, Harold M. "The Genus of an Algebraic Curve." In Essays in Constructive Mathematics. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-98558-5_4.

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Orzech, Grace, and Morris Orzech. "The Genus of a Nonsingular Plane Curve." In Plane Algebraic Curves. CRC Press, 2024. https://doi.org/10.1201/9781003573517-13.

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Schreyer, Frank-Olaf. "The geometric genus of a plane curve." In Universitext. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-84834-6_15.

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Sasikaladevi, N., A. Revathi, N. Mahalakshmi, and N. Archana. "HEAP- Genus 2 HyperElliptic Curve Based Biometric Audio Template Protection." In Communications in Computer and Information Science. Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-1810-8_31.

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Auffarth, Robert, Sebastián Reyes-Carocca, and Anita M. Rojas. "On the Jacobian Variety of the Accola-Maclachlan Curve of Genus Four." In Trends in Mathematics. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-77050-0_1.

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Cohn, Harvey. "A Numerical Survey of the Reduction of Modular Curve Genus by Fricke’s Involutions." In Number Theory. Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4757-4158-2_4.

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Kitamura, Izuru, Masanobu Katagi, and Tsuyoshi Takagi. "A Complete Divisor Class Halving Algorithm for Hyperelliptic Curve Cryptosystems of Genus Two." In Information Security and Privacy. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11506157_13.

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Guillevic, Aurore, and Damien Vergnaud. "Genus 2 Hyperelliptic Curve Families with Explicit Jacobian Order Evaluation and Pairing-Friendly Constructions." In Pairing-Based Cryptography – Pairing 2012. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36334-4_16.

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Conference papers on the topic "Curve genus"

1

Zhou, Hong, and Nisar Ahmed. "Synthesis of Path Generation Compliant Mechanisms Using Variable Width Spline Curves." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-36815.

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Path generation is to guide a point tracing a prescribed path. Compliant mechanisms (CMs) have been synthesized for path generation mechanisms. In this paper, each connection in a synthesized CM is represented as a variable width spline curve and the entire synthesized CM is modeled as a set of variable width spline curves. The synthesis of a path generation CM is systemized as the optimization of control parameters of a set of variable width spline curves. A variable width spline curve is a center spline curve with variable perpendicular width. The center spline curve is for the shape descrip

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2

Pelzl, J., T. Wollinger, and C. Paar. "High performance arithmetic for special hyperelliptic curve cryptosystems of genus two." In International Conference on Information Technology: Coding and Computing, 2004. Proceedings. ITCC 2004. IEEE, 2004. http://dx.doi.org/10.1109/itcc.2004.1286706.

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Bertoni, G., L. Breveglieri, T. Wollinger, and C. Paar. "Finding optimum parallel coprocessor design for genus 2 hyperelliptic curve cryptosystems." In International Conference on Information Technology: Coding and Computing, 2004. Proceedings. ITCC 2004. IEEE, 2004. http://dx.doi.org/10.1109/itcc.2004.1286710.

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Fang, Yuejian, and Zhonghai Wu. "A New Parallel Processor Architecture for Genus 2 Hyperelliptic Curve Cryptosystems." In 2012 IEEE Computer Society Annual Symposium on VLSI (ISVLSI). IEEE, 2012. http://dx.doi.org/10.1109/isvlsi.2012.24.

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Wang, Chen, and Hongbo Jiang. "SURF: A connectivity-based space filling curve construction algorithm in high genus 3D surface WSNs." In IEEE INFOCOM 2015 - IEEE Conference on Computer Communications. IEEE, 2015. http://dx.doi.org/10.1109/infocom.2015.7218470.

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Abhau, Jochen, Carl-Friedrich Bödigheimer та Ralf Ehrenfried. "Homology of the mapping class group Γ2,1 for surfaces of genus 2 with a boundary curve". У Conference in honour of Heiner Zieschang. Mathematical Sciences Publishers, 2008. http://dx.doi.org/10.2140/gtm.2008.14.1.

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Gutierrez, Jaime, D. Sevilla, and T. Shaska. "Hyperelliptic curves of genus 3 with prescribed automorphism group." In Computational Aspects of Algebraic Curves. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701640_0009.

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Shaska, T. "Genus two curves covering elliptic curves: a computational approach." In Computational Aspects of Algebraic Curves. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701640_0013.

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Demirbas, Yasin. "Hyperelliptic curves of genus 3 and 4 in characteristic 2." In Computational Aspects of Algebraic Curves. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701640_0011.

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Babu, H., and P. Venkataraman. "Group action on genus 3 curves and their Weierstrass points." In Computational Aspects of Algebraic Curves. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701640_0017.

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Reports on the topic "Curve genus"

1

Weller, Joel I., Harris A. Lewin, and Micha Ron. Determination of Allele Frequencies for Quantitative Trait Loci in Commercial Animal Populations. United States Department of Agriculture, 2005. http://dx.doi.org/10.32747/2005.7586473.bard.

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Individual loci affecting economic traits in dairy cattle (ETL) have been detected via linkage to genetic markers by application of the granddaughter design in the US population and the daughter design in the Israeli population. From these analyses it is not possible to determine allelic frequencies in the population at large, or whether the same alleles are segregating in different families. We proposed to answer this question by application of the "modified granddaughter design", in which granddaughters with a common maternal grandsire are both genotyped and analyzed for the economic traits.

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Wagner, D. Ry, Eliezer Lifschitz, and Steve A. Kay. Molecular Genetic Analysis of Flowering in Arabidopsis and Tomato. United States Department of Agriculture, 2002. http://dx.doi.org/10.32747/2002.7585198.bard.

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The primary objectives for the US lab included: the characterization of ELF3 transcription and translation; the creation and characterization of various transgenic lines that misexpress ELF3; defining genetic pathways related to ELF3 function regulating floral initiation in Arabidopsis; and the identification of genes that either interact with or are regulated by ELF3. Light quality, photoperiod, and temperature often act as important and, for some species, essential environmental cues for the initiation of flowering. However, there is relatively little information on the molecular mechanisms

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