Symmetries and exotic smooth structures on a $K3$ surface
| dc.creator | Chen, Weimin | |
| dc.creator | Kwasik, Slawomir | |
| dc.date | 2007-09-11 | |
| dc.date | 2008-09-11 | |
| dc.date.accessioned | 2026-07-07T10:01:49Z | |
| dc.date.available | 2026-07-07T10:01:49Z | |
| dc.description | 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. | |
| dc.description | 46 pages, final version, Journal of Topology, to appear | |
| dc.identifier | https://arxiv.org/abs/0709.1710 | |
| dc.identifier | http://arxiv.org/abs/0709.1710 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168761 | |
| dc.subject | Geometric Topology | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 57S15, 57R55 (Primary) 57R17 (Secondary) | |
| dc.title | Symmetries and exotic smooth structures on a $K3$ surface | |
| dc.type | text |