Borcherds products and arithmetic intersection theory on Hilbert modular surfaces
Number Theory
2007-05-23 v3 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.math/0310201,
title = {Borcherds products and arithmetic intersection theory on Hilbert modular surfaces},
author = {Jan H. Bruinier and Jose I. Burgos Gil and Ulf Kuehn},
journal= {arXiv preprint arXiv:math/0310201},
year = {2007}
}
Comments
71 pages, Theorems 6.7 and 6.8 added, references updated, some typos removed