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arXiv:0812.4518 [math.AG]AbstractReferencesReviewsResources

The dihedral group $\Dh_5$ as group of symplectic automorphisms on K3 surfaces

Alice Garbagnati

Published 2008-12-24, updated 2010-07-07Version 2

We prove that if a K3 surface $X$ admits $\Z/5\Z$ as group of symplectic automorphisms, then it actually admits $\Dh_5$ as group of symplectic automorphisms. The orthogonal complement to the $\Dh_5$-invariants in the second cohomology group of $X$ is a rank 16 lattice, $L$. It is known that $L$ does not depend on $X$: we prove that it is isometric to a lattice recently described by R. L. Griess Jr. and C. H. Lam. We also give an elementary construction of $L$.

Comments: 11 pages. Arguments revised, results unchanged. Final version, to appear in Proc. Amer. Math. Soc
Categories: math.AG
Subjects: 14J28, 14J50
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