Cubic Surfaces and Borcherds Products

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The moduli space of cubic surfaces in complex projective space is known to be isomorphic to the quotient of the complex 4-ball by a certain arithmetic group. We apply Borcherds' techniques to construct automorphic forms for this group and show that these provide an embedding of the moduli space in 9-dimensional projective space. We also show that our automorphic forms directly encode the geometry of cubic surfaces, by showing that each of Cayley's invariants (certain cross-ratios) is simply a quotient of two of our automorphic forms.
27 pages; plain TeX

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Algebraic Geometry, 11F55; 14J10

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http://salesiana.dossiersoluciones.com/handle/123456789/58656

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0002066
 http://arxiv.org/abs/math/0002066

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arXiv