Borcherds products and arithmetic intersection theory on Hilbert modular surfaces
Bruinier, Jan H. ; Burgos Gil, José I. ; Kühn, Ulf
Duke Math. J., Tome 136 (2007) no. 1, p. 1-88 / Harvested from Project Euclid
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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
Publié le : 2007-07-15
Classification:  11G18,  11F41,  14C17,  14G40,  14C20 
@article{1184341238,
     author = {Bruinier, Jan H. and Burgos Gil, Jos\'e I. and K\"uhn, Ulf},
     title = {Borcherds products and arithmetic intersection theory on Hilbert modular surfaces},
     journal = {Duke Math. J.},
     volume = {136},
     number = {1},
     year = {2007},
     pages = { 1-88},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1184341238}
}

Bruinier, Jan H.; Burgos Gil, José I.; Kühn, Ulf. Borcherds products and arithmetic intersection theory on Hilbert modular surfaces. Duke Math. J., Tome 136 (2007) no. 1, pp.  1-88. http://gdmltest.u-ga.fr/item/1184341238/