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15 July 2007 Borcherds products and arithmetic intersection theory on Hilbert modular surfaces
Jan H. Bruinier, José I. Burgos Gil, Ulf Kühn
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Duke Math. J. 139(1): 1-88 (15 July 2007). DOI: 10.1215/S0012-7094-07-13911-5

Abstract

We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying that Hirzebruch-Zagier divisors on a Hilbert modular surface are the coefficients of an elliptic modular form of weight 2. Moreover, we determine the arithmetic self-intersection number of the line bundle of modular forms equipped with its Petersson metric on a regular model of a Hilbert modular surface, and we study Faltings heights of arithmetic Hirzebruch-Zagier divisors

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Jan H. Bruinier. José I. Burgos Gil. Ulf Kühn. "Borcherds products and arithmetic intersection theory on Hilbert modular surfaces." Duke Math. J. 139 (1) 1 - 88, 15 July 2007. https://doi.org/10.1215/S0012-7094-07-13911-5

Information

Published: 15 July 2007
First available in Project Euclid: 13 July 2007

zbMATH: 1208.11077
MathSciNet: MR2322676
Digital Object Identifier: 10.1215/S0012-7094-07-13911-5

Subjects:
Primary: 11G18
Secondary: 11F41 , 14C17 , 14C20 , 14G40

Rights: Copyright © 2007 Duke University Press

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Vol.139 • No. 1 • 15 July 2007
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