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.
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) |
Keywords:
fake projective plane; surface of general type; Dolgachev surface; properly elliptic surface; fundamental groupCitations:
Zbl 1253.14034References:
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