Borcherds products and arithmetic intersection theory on Hilbert modular surfaces

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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 two. 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 study Faltings heights of arithmetic Hirzebruch-Zagier divisors.
71 pages, Theorems 6.7 and 6.8 added, references updated, some typos removed

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Number Theory, Algebraic Geometry, 11F41, 14C17, 14G40, 14C20, 11G18

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http://salesiana.dossiersoluciones.com/handle/123456789/68845

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0310201
 http://arxiv.org/abs/math/0310201

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arXiv