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Quotients of fake projective planes. (English) Zbl 1222.14088

Summary: Recently, G. Prasad and S.-K. Yeung [Invent. Math. 168, No. 2, 321–370 (2007; Zbl 1253.14034)] classified all possible fundamental groups of fake projective planes. According to their result, many fake projective planes admit a nontrivial group of automorphisms, and in that case it is isomorphic to \(\mathbb Z/3\mathbb Z, \mathbb Z/7\mathbb Z, 7:3\) or \((\mathbb Z; 3\mathbb Z)^2\), where \(7:3\) is the unique nonabelian group of order 21.
Let \(G\) be a group of automorphisms of a fake projective plane \(X\). In this paper we classify all possible structures of the quotient surface \(X/G\) and its minimal resolution.

MSC:

14J29 Surfaces of general type
14J27 Elliptic surfaces, elliptic or Calabi-Yau fibrations
14E15 Global theory and resolution of singularities (algebro-geometric aspects)

Citations:

Zbl 1253.14034
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References:

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