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Campedelli surfaces with fundamental group of order 8

Authors:	Margarida Mendes Lopes Rita Pardini Miles Reid

Institution:	(1) Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal;(2) Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo, 5, 56127 Pisa, Italy;(3) Math Institute, University of Warwick, Coventry, CV4 7AL, UK

Abstract:	Let S be a Campedelli surface (a minimal surface of general type with p _g = 0, K ² = 2), and ${\pi\colon Y\to S}$ an etale cover of degree 8. We prove that the canonical model ${\overline {Y}}$ of Y is a complete intersection of four quadrics ${\overline {Y}=Q_{1}\cap Q_{2}\cap Q_{3}\cap Q_{4}\subset\mathbb{P}^{6}}$ . As a consequence, Y is the universal cover of S, the covering group G = Gal(Y/S) is the topological fundamental group π ₁ S and G cannot be the dihedral group D ₄ of order 8. The first author is a member of the Centre for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Lisboa. The second is a member of G.N.S.A.G.A.–I.N.d.A.M.

Keywords:	Campedelli surfaces Surfaces with p g = 0 Fundamental group Group actions on surfaces
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