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2007

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/9171

Borcherds products and arithmetic intersection theory on Hilbert modular surfaces

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http://dx.doi.org/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 selfintersection 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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Geometria algebraica aritmètica, Teoria de la intersecció

Subject (English)

Arithmetic aspects of modular and Shimura varieties, Hilbert modular surfaces, Intersection theory, Arithmetic varieties and schemes

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Articles publicats en revistes (Matemàtiques i Informàtica)

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BRUINIER, Jan H. (Jan Hendrik), BURGOS GIL, José I. and KÜHN, Ulf. Borcherds products and arithmetic intersection theory on Hilbert modular surfaces. Duke Mathematical Journal. 2007. Vol. 139, num. 1, pags. 1-88. ISSN 0012-7094. [consulted: 7 of June of 2026]. Available at: https://hdl.handle.net/2445/9171

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