Uniruledness of orthogonal modular varieties
Authors:
V. Gritsenko and K. Hulek
Journal:
J. Algebraic Geom. 23 (2014), 711-725
DOI:
https://doi.org/10.1090/S1056-3911-2014-00632-9
Published electronically:
February 21, 2014
MathSciNet review:
3263666
Full-text PDF
Abstract | References | Additional Information
Abstract: A strongly reflective modular form with respect to an orthogonal group of signature determines a Lorentzian Kac-Moody algebra. We find a new geometric application of such modular forms: we prove that if the weight is larger than
, then the corresponding modular variety is uniruled. We also construct new reflective modular forms and thus provide new examples of uniruled moduli spaces of lattice polarised
surfaces. Finally, we prove that the moduli space of Kummer surfaces associated to
-polarised abelian surfaces is uniruled.
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Additional Information
V. Gritsenko
Affiliation:
Université Lille 1, Laboratoire Paul Painlevé, F-59655 Villeneuve d’Ascq, Cedex, France; and Institut Universitaire de France
Email:
Valery.Gritsenko@math.univ-lille1.fr
K. Hulek
Affiliation:
Institut für Algebraische Geometrie, Leibniz Universität Hannover, D-30060 Hannover, Germany
Email:
hulek@math.uni-hannover.de
DOI:
https://doi.org/10.1090/S1056-3911-2014-00632-9
Received by editor(s):
February 16, 2012
Received by editor(s) in revised form:
August 24, 1012
Published electronically:
February 21, 2014
Article copyright:
© Copyright 2014
University Press, Inc.