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Borcherds products and arithmetic intersection theory on Hilbert modular surfaces

2007; Duke University Press; Volume: 139; Issue: 1 Linguagem: Inglês

10.1215/s0012-7094-07-13911-5

1547-7398

Jan Hendrik Bruinier, José Ignacio Burgos Gil, Ulf Kühn,

Algebraic structures and combinatorial models

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