A new model for the theta divisor of the cubic threefold

2004/03/15 by Michela Artebani, Remke Kloosterman, Artebani, Michela +3
Mathematics · #14H10 #14H40 #14H50 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14H10 #msc:14H40 #msc:14H50

paper · pdf · doi:10.48550/arxiv.math/0403245

arxiv created 2004/03/15 · arxiv updated 2009/12/01

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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