Twists of genus three Jacobians

Details Twists of genus three Jacobians Twists of genus three Jacobians

2007-11-03

arxiv.org/abs/0711.0415v3

Mathematics

Algebraic Geometry

Scientific paper

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.

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