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Transactions of the American Mathematical Society

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Heegner divisors in the moduli space of genus three curves

Author: Michela Artebani
Journal: Trans. Amer. Math. Soc. 360 (2008), 1581-1599
MSC (2000): Primary 14J10, 14J28, 14H10
Published electronically: October 22, 2007
MathSciNet review: 2357706
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Abstract: S. Kondo 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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Additional Information

Michela Artebani
Affiliation: Dipartimento di Matematica, Università di Milano, via C. Saldini 50, 20133 Milano, Italia

Keywords: Genus three curves, splitting curves, $K3$ surfaces, Heegner divisors
Received by editor(s): October 12, 2005
Received by editor(s) in revised form: February 20, 2006
Published electronically: October 22, 2007
Additional Notes: This work was partially supported by PRIN 2003: Spazi di moduli e teoria di Lie; GNSAGA
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.