Arithmetic of a fake projective plane and related elliptic surfaces

Details Arithmetic of a fake projective plane and related elliptic surfaces Arithmetic of a fake projective plane and related elliptic surfaces

2008-03-05

arxiv.org/abs/0803.0645v3

Mathematics

Algebraic Geometry

15 pages, proofs of proposition 4.1 and lemma 5.1 improved, one remark added, some typing errors removed

Scientific paper

The purpose of the present paper is to explain the fake projective plane constructed by J.H. Keum from the point of view of arithmetic ball quotients. Beside the ball quotient associated with the fake projective plane, we also analize two further naturally related ball quotients whose minimal desingularizations lead to two elliptic surfaces, one already considered by J.H. Keum as well as the one constructed by M.N. Ishida in terms of p-adic uniformization.

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