2000/02/09 by Daniel Allcock, Allcock, Daniel, Eberhard Freitag +1
Mathematics · #11F55 #14J10 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:11F55 #msc:14J10
paper · pdf · doi:10.48550/arxiv.math/0002066
27 pages; plain TeX
arxiv created 2000/02/09 · arxiv updated 2009/11/30
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.