Flexibility of affine cones over del Pezzo surfaces of degree 4 and 5

TL;DR

This paper proves that the special automorphism group acts infinitely transitively on affine cones over del Pezzo surfaces of degrees 4 and 5, revealing a high level of symmetry in these geometric structures.

Contribution

It establishes the infinite transitivity of automorphism groups on affine cones over specific del Pezzo surfaces, a novel result in algebraic geometry.

Findings

Automorphism groups act infinitely transitively on the cones.

Affine cones over degree 4 and 5 del Pezzo surfaces exhibit high symmetry.

New insights into the automorphism groups of these geometric objects.

Abstract

We prove that the action of the special automorphism group on affine cones over del Pezzo surfaces of degree 4 and 5 is infinitely transitive.