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 H^2(X,\Z)which is fixed by the isometries induced by G. However for certain groups these discriminants are not the same as those found for explicit examples. Here we describe Kummer surfaces for which this phenomena happens and we explain the difference.
Symplectic automorphisms on Kummer surfaces / A. Garbagnati. - In: GEOMETRIAE DEDICATA. - ISSN 0046-5755. - 145:1(2010 Apr), pp. 219-232. [10.1007/s10711-009-9420-z]
Symplectic automorphisms on Kummer surfaces
A. Garbagnati
Primo
2010
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 H^2(X,\Z)which is fixed by the isometries induced by G. However for certain groups these discriminants are not the same as those found for explicit examples. Here we describe Kummer surfaces for which this phenomena happens and we explain the difference.
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