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.

arXiv comment17 pages; this version includes a part of the old one properly related to the title. The last part devoted to the automorphism groups was reworked and will appear in a separate preprint

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