Twists of genus three Jacobians
Algebraic Geometry
2015-05-13 v4 Number Theory
Abstract
We give a criterion to distinguish between a genus three Jacobian and its [-1] twist in terms of the product of the 36 even theta nulls. We also express the product of the 36 theta nulls in terms of the discriminant of a genus three curve. The results are arithmetic in nature and thus add to previous work over C on the product of the even theta nulls. They generalize previous work of Ritzenthaler and Lachaud for Abelian threefolds which are (2,2,2) isogenous to a product of elliptic curves. This answers a 2003 of letter of Jean-Pierre Serre to Jaap Top.
Keywords
Cite
@article{arxiv.0711.0415,
title = {Twists of genus three Jacobians},
author = {Stephen Meagher},
journal= {arXiv preprint arXiv:0711.0415},
year = {2015}
}