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A new model for the theta divisor of the cubic threefold

Michela Artebani·Remke Kloosterman·Marco Pacini
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Abstract

In this paper we give a birational model for the theta divisor of the intermediate Jacobian of a generic cubic threefold $X$. We use the standard realization of $X$ as a conic bundle and a $4-$dimensional family of plane quartics which are totally tangent to the discriminant quintic curve of such a conic bundle structure. The additional data of an even theta characteristic on the curves in the family gives us a model for the theta divisor.

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Michela Artebani, Remke Kloosterman, Marco Pacini. 2004-03-15. A new model for the theta divisor of the cubic threefold. https://arxiv.org/abs/math/0403245

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