Cones of Heegner divisors

Bruinier, Jan; Möller, Martin

doi:10.1090/jag/734

Authors: Jan Hendrik Bruinier and Martin Möller
Journal: J. Algebraic Geom. 28 (2019), 497-517
DOI: https://doi.org/10.1090/jag/734
Published electronically: April 11, 2019
MathSciNet review: 3959069
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Abstract | References | Additional Information

Abstract: We show that the cone of primitive Heegner divisors is finitely generated for many orthogonal Shimura varieties, including the moduli space of polarized $K3$-surfaces. The proof relies on the growth of coefficients of modular forms.

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Additional Information

Jan Hendrik Bruinier
Affiliation: Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstrasse 7, D–64289 Darmstadt, Germany
MR Author ID: 641446
Email: bruinier@mathematik.tu-darmstadt.de

Martin Möller
Affiliation: Institut für Mathematik, Goethe–Universität Frankfurt, Robert-Mayer-Str. 6–8, 60325 Frankfurt am Main, Germany
Email: moeller@math.uni-frankfurt.de

Received by editor(s): May 21, 2017
Received by editor(s) in revised form: July 9, 2018
Published electronically: April 11, 2019
Additional Notes: The first author was partially supported by DFG grant BR-2163/4-2. Both authors were supported by the LOEWE research unit “Uniformized structures in arithmetic and geometry”.
Article copyright: © Copyright 2019 University Press, Inc.