Isometry of K3 surface. - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T13:58:31Z http://mathoverflow.net/feeds/question/117631 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/117631/isometry-of-k3-surface Isometry of K3 surface. Zheng 2012-12-30T14:30:44Z 2013-02-10T18:22:00Z <p>Let $S$ be a K3 surface and $\iota$ be anti-symplectic involution of $S$. Suppose that $g$ is a Kahler-Einstein metric on $S$. My question is; </p> <blockquote> <p>Why $\iota$ is an isometry of $S$ with respect to $g$? Is this true for any holomorphic action of $S$? </p> </blockquote> <p><strong>Edit</strong> $\iota$ is called anti-symplectic if it acts on $\Omega^{2,0}$ as $-id$. </p> http://mathoverflow.net/questions/117631/isometry-of-k3-surface/117646#117646 Answer by Johannes Nordström for Isometry of K3 surface. Johannes Nordström 2012-12-30T16:03:44Z 2012-12-30T16:03:44Z <p>There is a unique Ricci-flat Kähler metric in each Kähler class of $S$. Thus, for any holomorphic automorphism $\iota$ of $S$, a Ricci-flat Kähler metric $g$ is invariant under $\iota$ if and only if its Kähler class $[\omega_g] \in H^{1,1}(S)$ is.</p>