Flexibility of Affine cones over Mukai fourfolds of genus $g\ge7$

TL;DR

This paper proves that affine cones over general Mukai fourfolds of genus 7, 8, and 9 are flexible, exhibiting infinite transitivity of their automorphism groups and showing they are A2-cylindrical.

Contribution

It establishes the flexibility and infinite transitivity of automorphism groups for affine cones over Mukai fourfolds of specific genera, a new result in algebraic geometry.

Findings

Affine cones over Mukai fourfolds of genus 7, 8, 9 are flexible.

Such cones admit infinitely transitive automorphism group actions.

Mukai fourfolds of these genera are A2-cylindrical.

Abstract

We show that the affine cones over a general Fano-Mukai fourfold of genus $g=7$, $8$ and $9$ are flexible. Equivalently, there is an infinitely transitive action of the special automorphism group on such affine cones. In particular, any Mukai fourfold of genus $7,8$ and $9$ is $\Bbb A^2$-cylindrical.