Geometriae Dedicata

, Volume 139, Issue 1, pp 49–55

Campedelli surfaces with fundamental group of order 8

Original Paper

DOI: 10.1007/s10711-008-9317-2

Cite this article as:
Mendes Lopes, M., Pardini, R. & Reid, M. Geom Dedicata (2009) 139: 49. doi:10.1007/s10711-008-9317-2

Abstract

Let S be a Campedelli surface (a minimal surface of general type with pg = 0, K2 = 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 π1S and G cannot be the dihedral group D4 of order 8.

Keywords

Campedelli surfaces Surfaces with pg = 0 Fundamental group Group actions on surfaces 

Mathematics Subject Classification (2000)

14J29 

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Margarida Mendes Lopes
    • 1
  • Rita Pardini
    • 2
  • Miles Reid
    • 3
  1. 1.Departamento de Matemática, Instituto Superior TécnicoUniversidade Técnica de LisboaLisboaPortugal
  2. 2.Dipartimento di MatematicaUniversità di PisaPisaItaly
  3. 3.Math InstituteUniversity of WarwickCoventryUK

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