Moduli of plane quartics, Gopel invariants and Borcherds products

Details Moduli of plane quartics, Gopel invariants and Borcherds products Moduli of plane quartics, Gopel invariants and Borcherds products

2009-06-15

arxiv.org/abs/0906.2598v1

Mathematics

Algebraic Geometry

Scientific paper

It is known that the moduli space of plane quartic curves is birational to an arithmetic quotient of a 6-dimensional complex ball. In this paper, we shall show that there exists a 15-dimensional space of meromorphic automorphic forms on the complex ball which gives a birational embedding of the moduli space of plane quartics with level 2 structure into 14-dimensional projective space. This map coincides with the one given by Coble by using Gopel invariants.

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