The dihedral group as a group of symplectic automorphisms on K3 surfaces

Author:
Alice Garbagnati

Journal:
Proc. Amer. Math. Soc. **139** (2011), 2045-2055

MSC (2010):
Primary 14J28, 14J50

DOI:
https://doi.org/10.1090/S0002-9939-2011-10650-6

Published electronically:
January 11, 2011

MathSciNet review:
2775382

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Abstract: We prove that if a K3 surface admits as a group of symplectic automorphisms, then it actually admits as a group of symplectic automorphisms. The orthogonal complement to the -invariants in the second cohomology group of is a rank 16 lattice, . It is known that does not depend on : 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 .

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Additional Information

**Alice Garbagnati**

Affiliation:
Dipartimento di Matematica, Università di Milano, via Saldini 50, I-20133 Milano, Italia

Email:
alice.garbagnati@unimi.it

DOI:
https://doi.org/10.1090/S0002-9939-2011-10650-6

Keywords:
K3 surfaces,
symplectic automorphisms,
dihedral groups,
lattices.

Received by editor(s):
August 18, 2009

Received by editor(s) in revised form:
February 5, 2010, June 3, 2010, and June 15, 2010

Published electronically:
January 11, 2011

Communicated by:
Ted Chinburg

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.