Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Borcherds products and arithmetic intersection theory on Hilbert modular
  surfaces   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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The categories of this paper are: bayes-an
3
The categories of this paper are: physics
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The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: econ
31
The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin