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Borcherds products and arithmetic intersection theory on Hilbert modular surfaces

Jan H. Bruinier·Jose I. Burgos Gil·Ulf Kuehn
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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 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.

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Jan H. Bruinier, Jose I. Burgos Gil, Ulf Kuehn. 2004-09-28. Borcherds products and arithmetic intersection theory on Hilbert modular surfaces. https://arxiv.org/abs/math/0310201

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