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arXiv · 0711.0415

Twists of genus three Jacobians

Stephen Meagher
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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.

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Stephen Meagher. 2007-11-03. Twists of genus three Jacobians. https://arxiv.org/abs/0711.0415

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