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Transactions of the American Mathematical Society

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ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Heegner divisors in the moduli space of genus three curves
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by Michela Artebani PDF
Trans. Amer. Math. Soc. 360 (2008), 1581-1599 Request permission

Abstract:

S. Kondō 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
  • MR Author ID: 744997
  • Email: michela.artebani@unimi.it, artebani@mat.unimi.it
  • 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
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 1581-1599
  • MSC (2000): Primary 14J10, 14J28, 14H10
  • DOI: https://doi.org/10.1090/S0002-9947-07-04280-8
  • MathSciNet review: 2357706