Symmetries and exotic smooth structures on a $K3$ surface

Details Symmetries and exotic smooth structures on a $K3$ surface Symmetries and exotic smooth structures on a $K3$ surface

2007-09-11

arxiv.org/abs/0709.1710v3

Mathematics

Geometric Topology

46 pages, final version, Journal of Topology, to appear

Scientific paper

Smooth and symplectic symmetries of an infinite family of distinct exotic $K3$ surfaces are studied, and 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, nonsmoothability of actions induced by a holomorphic automorphism of a prime order $\geq 7$ is proved and nonexistence of smooth actions by several $K3$ groups is established (included among which is the binary tetrahedral group $T_{24}$ which has the smallest order). Concerning symplectic symmetries, the fixed-point set structure of a symplectic cyclic action of a prime order $\geq 5$ is explicitly determined, provided that the action is homologically nontrivial.

Affiliated with

Also associated with

No associations

Rating

Symmetries and exotic smooth structures on a $K3$ surface does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Symmetries and exotic smooth structures on a $K3$ surface, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Symmetries and exotic smooth structures on a $K3$ surface will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-21495