Symplectic Automorphisms on Kummer Surfaces

Details Symplectic Automorphisms on Kummer Surfaces Symplectic Automorphisms on Kummer Surfaces

2008-02-04

arxiv.org/abs/0802.0369v1

Mathematics

Algebraic Geometry

13 pages

Scientific paper

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 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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