Siegel modular forms generated by invariants of cubic hypersurfaces

Details Siegel modular forms generated by invariants of cubic hypersurfaces Siegel modular forms generated by invariants of cubic hypersurfaces

1994-03-03

arxiv.org/abs/alg-geom/9403005v3

Mathematics

Algebraic Geometry

24 pages in AMSppt 2.1, preprint Univ. of Georgia 2/94

Scientific paper

We give a geometric derivation of Schottky's equation in genus four for the period matrices of Riemann surfaces among all period matrices. The equation arises naturally from the singularity theory of the Gauss map on the theta divisor, and thus generalizes for any genus $g \ge 4$ to a certain ideal of Siegel modular forms vanishing on period matrices of Riemann surfaces. This ideal is generated by modular forms associated to the invariants of cubic forms in $g - 1$ variables which vanish on the Fermat cubic.

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