## On K3 Surfaces Admitting Finite Non-Symplectic Group Actions

J. Math. Sci. Univ. Tokyo
Vol. 5 (1998), No. 2, Page 273--297.

Machida, Natsumi ; Oguiso, Keiji
On K3 Surfaces Admitting Finite Non-Symplectic Group Actions
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]

Abstract:
For a pair $(X, G)$ of a complex K3 surface $X$ and its finite automorphism group $G$, we call the value $I(X, G) := |\Im(G\rightarrow \Aut(H^{2,0}(X)))|$ the transcendental value and the Euler number $\varphi(I(X,G))$ of $I(X,G)$ the transcendental index. This paper classifies the pairs $(X,G)$ with the maximal transcendental index $20$ and the pair $(X,G)$ with $I(X,G) = 40$ up to isomorphisms. We also determine the set of transcendental values and apply this to determine the set of global canonical indices of complex projective threefolds with only canonical singularities and with numerically trivial canonical Weil divisor.

Mathematics Subject Classification (1991): Primary 14J28; Secondary 14J32, 14J50
Mathematical Reviews Number: MR1633933