Ga-actions on affine cones

TL;DR

This paper establishes a criterion for when unipotent group actions can exist on affine cones over projective varieties, expanding understanding of symmetries in algebraic geometry.

Contribution

It provides a new criterion for the existence of unipotent group actions on affine cones over projective varieties or quasicones.

Findings

Criterion for unipotent group actions on affine cones

Applicable to cones over projective and quasicones

Enhances understanding of algebraic group actions

Abstract

We give a criterion of existence of a unipotent group action on the affine cone over a projective variety or, more generally, on the affine quasicone over a variety which is projective over another affine variety.