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 $(2,n)$ 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 $n$, 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 $\mathrm {K3}$ surfaces. Finally, we prove that the moduli space of Kummer surfaces associated to $(1,21)$-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
MR Author ID:
219176
Email:
Valery.Gritsenko@math.univ-lille1.fr
K. Hulek
Affiliation:
Institut für Algebraische Geometrie, Leibniz Universität Hannover, D-30060 Hannover, Germany
MR Author ID:
89705
Email:
hulek@math.uni-hannover.de
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.
