Borcherds products and arithmetic intersection theory on Hilbert modular surfaces

By Jan H. Bruinier, Jose Ignacio Burgos Gil, U. Kuehn. 2003

76 citations recorded by the source corpus.

We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying that Hirzebruch-Zagier divisors on a Hilbert modular surface are the coecients of an elliptic modular form of weight two. 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 study Faltings heights of arithmetic Hirzebruch-Zagier divisors.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/54723c59f1584bdb6513b824352fd52bba7f6782

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Citations in the corpus

COHOMOLOGICAL ARITHMETIC CHOW RINGS (2004, methodology): “the axiomatic system and asking for the existence of a specialization morphism at the level of complexes. Applications. The theory developed in this paper is extensively used in the forthcoming paper [12] by J. Bruinier, J.I. Burgos and U. Ku¨hn, where explicit calculations for the arithmetic self-i”
Arithmetic characteristic classes of automorphic vector bundles (2005, methodology): “= Γ\B. It is expected that these arithmetic self-intersection numbers play an important role for possible extensions of the Gross-Zagier theorem to higher dimensions (cf. conjectures of S. Kudla). In [6], J. Bruinier, J. Burgos, and U. Ku¨hn used the theory developed in 4 [10] in order to obtain an ”
Faltings heights of CM cycles and derivatives of L-functions (2008, background): “(If the constant term c+(0,0) of f does not vanish, one actually has to work with the generalization of Arakelov geometry given in [13], see also [11].”