Affine cones over Fano-Mukai fourfolds of genus 10 are flexible

Abstract

We show that the affine cones over any Fano-Mukai fourfold of genus 10 are flexible; in particular, the automorphism group of such a cone acts highly transitively outside the vertex. Furthermore, any Fano-Mukai fourfold of genus 10, with one exception, admits a covering by open charts isomorphic to the affine four-space.