## 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)

Zbl 1253.14034
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### References:

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