Premium
Symmetries and exotic smooth structures on a K3 surface
Author(s) -
Chen Weimin,
Kwasik Slawomir
Publication year - 2008
Publication title -
journal of topology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.447
H-Index - 31
eISSN - 1753-8424
pISSN - 1753-8416
DOI - 10.1112/jtopol/jtn027
Subject(s) - mathematics , homogeneous space , symplectic geometry , automorphism , automorphism group , pure mathematics , holomorphic function , action (physics) , k3 surface , cyclic group , group (periodic table) , group action , order (exchange) , tetrahedron , heisenberg group , prime (order theory) , combinatorics , geometry , physics , quantum mechanics , abelian group , finance , economics , moduli space
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 T 24 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.