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.
A new model for the theta divisor of the cubic threefold / M. Artebani, K. R., P. M.. - In: LE MATEMATICHE. - ISSN 0373-3505. - 58:2(2003), pp. 201-236.
A new model for the theta divisor of the cubic threefold
M. ArtebaniPrimo
;
2003
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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