Symmetries and exotic smooth structures on a K3 surface | Zendy

Chen Weimin | Zendy; Kwasik Slawomir | Zendy

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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.

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