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Campedelli surfaces with fundamental group of order 8

2008; Springer Science+Business Media; Volume: 139; Issue: 1 Linguagem: Inglês

10.1007/s10711-008-9317-2

1572-9168

Margarida Mendes Lopes, Rita Pardini, Miles Reid,

Finite Group Theory Research

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.