Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fake projective planes   A fake projective plane is a smooth complex surface which is not the complex
projective plane but has the same Betti numbers as the complex projective
plane. The first example of such a surface was constructed by David Mumford in
1979 using p-adic uniformization. Two more examples were found by Ishida and
Kato by related method. Keum has recently given an example which is possibly
different from the three known earlier. It is an interesting problem in complex
algebraic geometry to determine all fake projective planes. Using the
arithmeticity of the fundamental group of fake projective planes, the formula
for the covolume of principal arithmetic subgroups given by the first-named
auhor, and some number theoretic estimates, we give a classification of fake
projective planes in this paper. Twenty eight distinct classes are found. The
construction given in the paper appears to be more direct and more natural. It
does not use p-adic uniformization.

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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: nucl-th