Infinite Genus Curves With Hyperelliptic Ends

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by S Erickson 2011 Cited by 9 [11, 3], only genus 2 and possibly genus 3 hyperelliptic curves might base divisor and the interpretation of the points at infinity appears to be very.

Explicit Construction of Rational Torsion Divisors on

by M Kronberg 2016 Cited by 1 Simplicity of Jacobians of Genus Two Hyperelliptic Curves Then the unique point at infinity of the projective closure of C is a K-rational Weier-.

Arithmetic of hyperelliptic curves - Bayreuth

by M Stoll Cited by 5 A hyperelliptic curve of genus g over a field k DEF hyperelliptic Otherwise there are no k-rational points at infinity (but there will.

Hyperelliptic curves with many automorphisms - People

by ND Müller 2017 Cited by 8 curve for each genus g ≥ 3. Furthermore, there are 15 hyperelliptic curves with many automorphisms which do not belong to the infinite families.65 pages

Explicit Construction of Rational Torsion Divisors on

by HM Kronberg Cited by 1 Simplicity of Jacobians of Genus Two Hyperelliptic Curves Then the unique point at infinity of the projective closure of C is a K-rational Weier-.


by T Kappeler 2017 Cited by 3 entials on hyperelliptic curves of infinite genus and obtain uniform -smooth curve in Xr that starts and ends at p.

Hyperelliptic Curves

24 Sep 2015 Suppose X : y2 = f (x) is hyperelliptic of genus g > 1. In what follows, we suppose f has odd degree, so X has a single point ∞ at infinity.

The infinite topology of the hyperelliptic locus in Torelli space

by K Kordek 2015 Cited by 2 Genus g Torelli space is the moduli space of genus g curves of compact needed for the proof of Theorem 1.1, which is given at the end of.

Doctorat ParisTech THÈSE Télécom ParisTech - l'ANSSI

by JP FLORI existence of infinite classes of Boolean functions with good cryptographic properties. 4.2.2 Exponential sums and hyperelliptic curves


by I Fischer 1956 Cited by 13 I, is an irreducible algebraic system of regular plane curves of genus g [1J4, p. 698, loc. cit.]. by infinitely many points on the moduli-variety.21 pages

2-Selmer groups of hyperelliptic curves with marked points

by A Shankar 2019 Cited by 6 this proportion goes to 1 as the genus goes to infinity. Consider a smooth hyperelliptic curve C1 of genus m ≥ 2 over Q, with a marked.38 pages

Relations Between Theta Functions of Genus One and Two

by T Hill 2018 t remarks at the end of this section describe the group struct ure on a genus 1 or elliptic curve. 5. Page 10. convention s,. 't9 00 ( Z; T) 


by J BOX 2019 Cited by 18 quadratic points on each modular curve X0(N) of genus 2, 3, 4, over Q to an elliptic curve with infinite Mordell Weil group (the existence of which 

Efficient Hyperelliptic Arithmetic using Balanced

by SD Galbraith Cited by 50 It is well-known that arithmetic on curves with two points at infinity In this paper we consider a genus g hyperelliptic curve C defined over a field K.


by JS Yelton 2015 Cited by 3 J is an elliptic curve. We then give a full desription of the infinite algebraic extension of K the Jacobian of a genus-2 hyperelliptic curve.

Numerical verification of Beilinson's conjecture for K 2 of

by T Dokchitser 2006 Cited by 33 quite difficult to write down enough elements in K2(C;Z), but we give several infinite families of hyperelliptic curves of genus 2 and 3 and one further 

On the Units of Coordinate Rings of Algebraic Curves

examples of genus-2 hyperelliptic curves over Q with nontrivial unit group end if;. First the curve gets computed and the points at infinity are defined 

Counting points on hyperelliptic curves in large - TEL (thèses

by S Abelard 2018 Cited by 6 Chapter 3 reviews previous work on point-counting over genus-2 curves, and finishes with an updated analysis on prospective and change that 

Constructing genus 3 hyperelliptic Jacobians with complex

by JS BALAKRISHNAN Cited by 24 several hyperelliptic curves of genus 3 with CM by sextic fields K. In to estimate the tail of the infinite series giving the theta constants so that we 

The number of hyperelliptic curves over a finite field. Recent

by L Hernández Encinas 2001 If c is a hyperelliptic curve of genus а defined over Fq, then the order of j (Fq), is tangent to the infinity line ф0 ] 0 at this point. If.

Quadratic points on modular curves - Universiteit Leiden

24 Nov 2017 Chapter 1 will finish by proving a theorem about how to classify all quadratic points of hyperelliptic curves of genus 2.

Hyperelliptic Curves and Their Jacobians

Let Γ be a compact Riemann surface of genus g. Then the dimen- sion of the space of all holomorphic differentials on Γ is equal to g. This theorem will be 


by S GRUSHEVSKY Cited by 4 Abstract. We construct an infinite number of Shimura curves contained in the locus of hyperelliptic Jacobians of genus 3. In the.

Hyperelliptic Curves - Department of Mathematics - The

10 Feb 2011 To see the points at infinity we will move them to points on a related The genus of the hyperelliptic curve is g = max{deg(H(x))−1,  34 pages


by HB DANIELS Cited by 10 Given an elliptic curve E/Q, the torsion points of E give rise to a natural Jones describe a genus 0 modular curve X (6) whose points correspond to 

Elliptic and hyperelliptic curves over supersimple fields

by A Martin-Pizarro 2014 Cited by 10 We prove that if F is an infinite field with characteristic The definition of a hyperelliptic curve often assumes the genus to be at.

Computing period matrices and the Abel-Jacobi - Hal-Inria

by P Molin 2019 Cited by 21 For hyperelliptic curves of arbitrary genus, the Magma implementation due to van C at infinity, that behave differently depending.

Normal Forms of Hyperelliptic Curves of Genus 3 - Home

by G Frey 2015 Cited by 3 By the theory of curves we know that non-hyperelliptic curves of genus 3 can be always be given by a plane equation of degree 4 and that 

Hyperelliptic Curves with Many Automorphisms - arXiv

by N Müller 2017 Cited by 8 Let X be a smooth connected projective algebraic curve of genus g ⩾ 2 over infinite families with ¯G cyclic or dihedral and 15 further 

On quadratic points of classical modular curves - Departament

by F BARS Cited by 9 The set of quadratic points is infinite: Hyperelliptic and defined over k, and if the genus 0 curve has no points over k (this situation only.

Geometry of Algebraic Curves

We want, however, a compact Riemann surface in the end. So for non-hyperelliptic curves of genus ≥ 2, the canonical divisor induces an imbed-.

On the Jacobian Varieties of Hyperelliptic Curves over Fields

by N Yui 1978 Cited by 119 matrix of the hyperelliptic curve C of genus g defined over K (with respect to (b) The endomorphism algebra ~22 = End,( J(C)) @Q is commutative and.

ON HYPERELLIPTIC JACOBIANS 1. Introduction In this article

by N BRUIN 2005 Cited by 25 Especially for hyperelliptic curves, this often enables the We derive an explicit parametrised infinite family of genus 2 curves whose.

Algorithms to enumerate superspecial Howe curves of genus 4

by M Kudo 2020 curves of genus 2 by gluing supersingular elliptic curves together along their 2-torsion [12, §3], and then the two genus-1 double covers to infinity.


by N BRUIN 2009 Cited by 87 curve C should have a rational point over the completion kv of k at v. For curves of genus 0, this is sufficient as well: if a genus 0 curve 


by P VAN MOERBEKE Cited by 255 However, the generic Hill's operator has an infinite number of bands and must be analyzed in terms of a hyperelliptic curve of infinite genus;.

Aspects of the arithmetic of uniquely trigonal genus four curves

by A Kulkarni 2018 an infinite family of cubic number fields whose class group has 2-rank 3.2 Del Pezzo surfaces, elliptic surfaces, and curves of genus 4: 

Counting in the Jacobian of Hyperelliptic Curves - mediaTUM

by S Sadanandan Cited by 1 In this example the genus of the curve is 2. The curve can be seen as the first curve in Figure 2.1. 6point at infinity is in the projective plane P2(L)  108 pages

unit equations and curves of genus with good reduction away

by J Rowan 2016 Cited by 1 hyperelliptic curves of genus 2 with good reduction outside 3 in a v) that is only checked implicitly at the very end (when curves.

Download - - University of

by C Maistret 2017 Cited by 5 2.1.3 Jacobians of hyperelliptic curves of genus 2 9 3.3 Computation of local invariants at infinite places 25.

Continued fractions and the divisor at infinity on a hyperelliptic

by K Daowsud 2013 Cited by 1 divisor at infinity on a hyperelliptic curve; and, (2) to apply a naive method to search for hyperelliptic curves of given genus g and order 

Rational points on curves

by M STOLL 2015 Cited by 31 of genus at least 2 over Q. We will use hyperelliptic curves two k-rational points at infinity, together with the affine points (ξ,η) 

Hanoi lectures on the arithmetic of hyperelliptic curves

by BH Gross 2012 Cited by 10 with a rational Weierstrass point. We end with a short discussion of hyperelliptic curves with two rational points at infinity.10 pages

Infinite Genus Riemann Surfaces - UBC Math

by J Feldman Cited by 17 So first we describe H(q) as an example of an infinite genus Riemann surface satisfying axioms (GH1-6) of the Appendix. Other examples, like Fermi curves or 

Rational points on curves - Numdam

by M Stoll 2011 Cited by 31 a computable finite set of points (coming from points at infinity and from elliptic curve, or more generally, on a genus 1 curve, would provide enough.

Infinite genus curves with hyperelliptic ends - Wiley Online

by MLDS Menezes 1989 Cited by 5 Infinite Genus Curves with Hyperelliptic Ends. MARIA LUCIA DA SILVA MENEZES For example, Hill's equation has been used to obtain hyperelliptic.

Elliptic factors in Jacobians of low genus curves - Mathematics

by JR PAULHUS Cited by 8 Appendix A Genus 3 and 4 Hyperelliptic Curve Data potent relations in End0(JX)=End(JX)⊗ZQ under the canonical map of Q-algebras from.

A discriminant and an upper bound for w2 for hyperelliptic

by I KAUSZ 1999 Cited by 36 We define a natural discriminant for a hyperelliptic curve X of genus g over a field K as a and ends at the unique vertex, is counted twice).

arXiv:1707.08676v5 [math.AG] 20 Feb 2020 - Épijournal de

by V Blankers 2020 Cited by 6 alizes work of Chen and Tarasca and establishes an infinite family of mula implies that a hyperelliptic curve of genus g contains 2g+2 

Dessins d'enfants and some holomorphic structures on the

7 Jun 2021 surface of infinite genus and exactly one end. If moreover, n = 2, the affine curve S(f ) is known as infinite hyperelliptic curve.