Symplectic Automorphisms on Kummer Surfaces

2008/02/04 by Alice Garbagnati, Garbagnati, Alice
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #math.AG #msc:14J28 #msc:14J50

paper · pdf · doi:10.48550/arxiv.0802.0369

13 pages

arxiv created 2008/02/04 · arxiv updated 2009/12/01

Abstract

Nikulin proved that the isometries induced on the second cohomology group of a K3 surface X by a finite abelian group G of symplectic automorphisms are essentially unique. Moreover he computed the discriminant of the sublattice of H²(X, \Z) which is fixed by the isometries induced by G. However for certain groups these discriminants are not the same of those found for explicit examples. Here we describe Kummer surfaces for which this phenomena happens and we explain the difference.

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• Elliptic fibrations and symplectic automorphisms on K3 surfaces

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