Theta constants associated to cubic three folds

Details Theta constants associated to cubic three folds Theta constants associated to cubic three folds

2000-08-03

arxiv.org/abs/math/0008024v1

Mathematics

Algebraic Geometry

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Scientific paper

For a cubic surface X, by considering the intermediate Jacobian J(Y) of the triple covering Y of the 3-dimensional projective space branching along X, Allcock, Carlson and Toledo constructed a period map per from the family of marked cubic surfaces to the four dimensional complex ball embedded in the Siegel upper half space of degree 5. We give an expression of the inverse of per in terms of theta constants by constructing an isomorphism between J(Y) and a Prym variety of a cyclic 6-ple covering of the projective line branching at seven points.

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