Borcherds products and arithmetic intersection theory on Hilbert modular surfaces

Details Borcherds products and arithmetic intersection theory on Hilbert modular surfaces Borcherds products and arithmetic intersection theory on Hilbert modular surfaces

2003-10-14

arxiv.org/abs/math/0310201v3

Mathematics

Number Theory

71 pages, Theorems 6.7 and 6.8 added, references updated, some typos removed

Scientific paper

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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