Symmetries and exotic smooth structures on a K3 surface

Authors

WM Chen, University of Massachusetts - AmherstFollow
S Kwasik

Publication Date

2008

Journal or Book Title

JOURNAL OF TOPOLOGY

Abstract

Smooth and symplectic symmetries of an infinite family of distinct exotic K3 surfaces are studied, and a comparison with the corresponding symmetries of the standard K3 is made. The action on the K3 lattice induced by a smooth finite group action is shown to be strongly restricted, and, as a result, the nonsmoothability of actions induced by a holomorphic automorphism of prime order at least 7 is proved, and the nonexistence of smooth actions by several K3 groups is established (included among which is the binary tetrahedral group T₂₄ that has the smallest order). Concerning symplectic symmetries, the fixed-point set structure of a symplectic cyclic action of prime order at least 5 is explicitly determined, provided that the action is homologically nontrivial.

Comments

This is the pre-published version harvested from ArXiv. The published version is located at http://jtopol.oxfordjournals.org/content/1/4/923.refs

Pages

923-962

Volume

1

Issue

4

Recommended Citation

Chen, WM and Kwasik, S, "Symmetries and exotic smooth structures on a K3 surface" (2008). JOURNAL OF TOPOLOGY. 268.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/268