Heegner divisors in the moduli space of genus three curves

Details Heegner divisors in the moduli space of genus three curves Heegner divisors in the moduli space of genus three curves

2005-10-10

arxiv.org/abs/math/0510199v1

Mathematics

Algebraic Geometry

Scientific paper

S. Kond\=o used periods of $K3$ surfaces to prove that the moduli space of genus three curves is birational to an arithmetic quotient of a complex 6-ball. In this paper we study Heegner divisors in the ball quotient, given by arithmetically defined hyperplane sections of the ball. We show that the corresponding loci of genus three curves are given by: hyperelliptic curves, singular plane quartics and plane quartics admitting certain rational "splitting curves".

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