arXiv Analytics

Sign in

arXiv:0902.0601 [math.AG]AbstractReferencesReviewsResources

Symplectic automorphisms and the Picard group of a K3 surface

Ursula Whitcher

Published 2009-02-03, updated 2010-05-11Version 3

We consider the symplectic action of a finite group G on a K3 surface. The Picard group of the K3 surface has a primitive sublattice determined by G. We show how to compute the rank and discriminant of this sublattice. We then describe moduli spaces of K3 surfaces with symplectic G-action, extending results of Nikulin in the abelian case. We use our moduli spaces to develop techniques for classifying all possible symplectic actions of a group G.

Comments: 10 pages; improved exposition in Section 3. To appear in Communications in Algebra.
Categories: math.AG
Subjects: 14J28
Related articles: Most relevant | Search more
arXiv:0812.4518 [math.AG] (Published 2008-12-24, updated 2010-07-07)
The dihedral group $\Dh_5$ as group of symplectic automorphisms on K3 surfaces
arXiv:math/0602358 [math.AG] (Published 2006-02-16)
On the Brill-Noether theory for K3 surfaces, II
arXiv:math/0205126 [math.AG] (Published 2002-05-12, updated 2005-05-25)
Some remarks about the FM-partners of K3 surfaces with Picard numbers 1 and 2

Links

Toolbox