Flexibility of normal affine horospherical varieties

TL;DR

This paper studies the flexibility property of affine varieties under group actions, proving it for smooth affine varieties with certain conditions and for normal affine horospherical varieties of complexity zero.

Contribution

It establishes the flexibility of smooth affine varieties with specific group actions and extends this property to normal affine horospherical varieties of complexity zero.

Findings

Smooth affine varieties with constant invertible functions and locally transitive reductive group actions are flexible.

Normal affine complexity-zero horospherical varieties are flexible.

Abstract

We investigate flexibility of affine varieties with an action of a linear algebraic group. Flexibility of a smooth affine variety with only constant invertible functions and a locally transitive action of a reductive group is proved. Also we show that a normal affine complexity-zero horospherical variety is flexible.