Explicit computations of Serre's obstruction for genus 3 curves and application to optimal curves
Author:
- Christophe RitzenthalerCRChristophe Ritzenthaler
Preprint
Abstract
Let k be a field of characteristic different from 2. There can be an obstruction for an indecomposable principally polarized abelian threefold (A,a) over k to be a Jacobian over k. It can be computed in terms of the rationality of the square root of the value of a certain Siegel modular form. We show how to do this explicitly for principally polarized abelian threefolds which are the third power of an elliptic curve with complex multiplication. We use our numeric results to prove or refute the existence of some optimal curves of genus 3.Keywords
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This publication has 6 references indexed in Scilit:
- On the Torelli problem and Jacobian Nullwerte in genus threeThe Michigan Mathematical Journal, 2011
- Curves of genus 3 over small finite fieldsIndagationes Mathematicae, 2003
- Classification of Hermitian Forms with the Neighbour MethodJournal of Symbolic Computation, 1998
- Abelian varieties over finite fieldsAnnales Scientifiques de lʼÉcole Normale Supérieure, 1969
- Modular Forms and Projective InvariantsAmerican Journal of Mathematics, 1967
- On Products and Algebraic Families of Jacobian VarietiesAnnals of Mathematics, 1963