Curves of genus 2 with split jacobian
WebAbstract. We decompose the Jacobian variety of hyperelliptic curves up to genus 20, de ned over an algebraically closed eld of characteristic zero, with reduced automorphism group A 4, S 4, or A 5: Among these curves is a genus 4 curve with Jacobian variety isogenous to E2 1 2E 2 and a genus 5 curve with Jacobian variety isogenous to E5, for … WebDec 5, 2012 · Yuri Zarhin. 4,990 19 30. Add a comment. 4. Every curve of genus 2 has an equation of the form Y 2 Z 4 = f 0 X 6 + f 1 X 5 Z + ⋯ + f 6 Z 6. ] Flynn (1990) has found the equations of the Jacobian variety of such a curve in characteristic ≠ 2, 3, 5 --- they form a set 72 homogeneous equations of degree 2 in 16 variables (they take 6 pages to ...
Curves of genus 2 with split jacobian
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WebApr 23, 2009 · Curves of genus 2 have an associated abelian surface, their jacobian. One can classify genus 2 curves according to special properties of their jacobians. For instance, a jacobian can be split: isogenous to a product of elliptic curves. There are several ways in which jacobians can be split. In this talk we will give a precise description of one ... Web2. Five-torsion on genus two Jacobians Let kbe a eld of characteristic di erent from 2;3 and let Cbe a smooth projective curve of genus 2 over kgiven by an a ne model C: y2 = F(x); where F(x) 2k[x] is of degree 5 or 6 (this only mildly restricts the admissible Cif kis a nite eld of 5 elements). Let Jbe the Jacobian of C.
WebSplit jacobian curves of genus 2 have also been used to exhibit nonisomorphic curves with the same jacobian; vide [3, 4]. The approach in these papers is through the … WebLet kbe a field and let Cbe a curve of genus 2 over k. Let J= Jac(C) be its Jacobian. The abelian variety is called decomposable over kif J is isogenous over kto a product of elliptic curves E1 × E2. A genus 2 curve has a decomposable Jacobian if and only if there is a cover φ1: C→ E1 to an elliptic curve E′. If we take φ
WebApr 17, 2024 · We will talk about the Ceresa class, which is the image under a cycle class map of a canonical homologically trivial algebraic cycle associated to a curve in its … Webto have a split Jacobian for some curves Cin positive characteristic (see e.g. discussion in [2]). In particular, one can have a Jacobian of the form J(C) = E 1 E 2;the sum of two …
WebSplit jacobian curves of genus 2 have also been used to exhibit nonisomorphic curves with the same jacobian; vide [3, 4]. The approach in these papers is through the algebraic geometry of abelian varieties, and the constructions are therefore far from explicit. …
WebJun 20, 2008 · In this article, we give a new proof of the existence of curves of genus 5 and 17 with split Jacobian by constructing explicit two families of such curves over number fields. Key Words: Algebraic curves Splitting of Jacobian variables. 2000 Mathematics Subject Classification: 14H40 14Q05. sonic chowderWebJan 1, 2002 · There are exactly six ℂ-isomorphism classes of genus two curves \mathcal {C} with Aut ( \mathcal {C} ) isomorphic to D 8 (resp., D 12) and with (3, 3)-split … small home office tableWebReferences. Athorne C., Eilbeck J.C., Enolskii V.Z., A ${\rm SL}(2)$ covariant theory of genus 2 hyperelliptic functions, Math. Proc. Cambridge Philos. Soc. 136 (2004 ... small home parksWebIn genus $2$, Calta and McMullen independently discovered an infinite family of algebraically primitive Teichmüller curves. However, in higher genus, such curves seem to be much rarer. We will discuss a result that shows that the regular $14$-gon yields the unique algebraically primitive Teichmüller curve in genus $3$ of a particular ... small home packagesWebGenus 2 Curves with (3,3)-Split Jacobian and Large Automorphism Group Tony Shaska UniversityofCaliforniaatIrvine,Irvine,CA92697. [email protected] … sonic christmas coloring pages printableWebWe discuss the Mordell-Weil sieve as a general technique for proving results concerning rational points on a given curve. In the special case of curves of genus 2, we describe quite explicitly how the relevant local in… small home photosWebJan 1, 2002 · Let C be a genus 2 curve defined over k, char (k)=0. If C has a (3,3)-split Jacobian then we show that the automorphism group Aut (C) is isomorphic to one of the … small home plans for seniors