Campedelli surfaces with fundamental group of order 8

Let S be a Campedelli surface (a minimal surface of general type with p g  = 0, K 2  = 2), and an etale cover of degree 8. We prove that the canonical model of Y is a complete intersection of four quadrics . As a consequence, Y is the universal cover of S , the covering group G  = Gal( Y / S ) is th...

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Bibliographic Details
Published in:Geometriae dedicata 2009-04, Vol.139 (1), p.49-55
Main Authors: Mendes Lopes, Margarida, Pardini, Rita, Reid, Miles
Format: Article
Language:English
Subjects:
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Hyperbolic Geometry
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Topology
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Summary:Let S be a Campedelli surface (a minimal surface of general type with p g  = 0, K 2  = 2), and an etale cover of degree 8. We prove that the canonical model of Y is a complete intersection of four quadrics . 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.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-008-9317-2