Moduli of Plane Quartics, Gopel Invariants and Borcherds Products

作者：Kondo Shigeyuki^*

来源：International Mathematics Research Notices, 2011, (12): 2825-2860.

DOI：10.1093/imrn/rnq190

It is known that the moduli space of plane quartic curves is birational to an arithmetic quotient of a six-dimensional complex ball [Kondo, S. "A complex hyperbolic structure of the moduli space of curves of genus three." Journal fur die Reine und Angewandte Mathematik 525 (2000): 219-32]. 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 . This map coincides with the one given by Coble ["Algebraic geometry and theta functions." Algebraic geometry and theta functions. American Mathematical Society Colloquium Publication 10. Providence, RI: American Mathematical Society, 1929 (3rd ed., 1969)] by using Gopel invariants.

• 出版日期2011