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Working paper

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

Prokhorov Y., Zaidenberg M.
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.