Affine cones over cubic surfaces are flexible in codimension one

TL;DR

This paper proves that affine cones over certain smooth cubic surface polarizations exhibit flexibility in codimension one, meaning they have rich automorphism groups acting transitively on large open subsets.

Contribution

It establishes the flexibility of affine cones over specific del Pezzo surfaces of degree 3 with non-anticanonical polarization, expanding understanding of automorphism group actions.

Findings

Affine cones over these surfaces are flexible in codimension one.

Such cones admit an infinitely transitive special automorphism group action.

The result applies to polarizations not proportional to the anticanonical divisor.

Abstract

Let Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension one. Equivalently, such a cone has an open subset with an infinitely transitive action of the special automorphism group on it.