Generically flexible affine varieties with invariant divisors

TL;DR

This paper constructs higher-dimensional affine varieties with a large automorphism group acting with an open orbit, where the complement of the orbit has codimension one, revealing new examples of flexible algebraic structures.

Contribution

It provides explicit examples of affine varieties with a large automorphism group acting with an open orbit and a divisor complement, expanding understanding of automorphism group actions.

Findings

Existence of affine varieties with automorphism groups acting with open orbits

Construction of examples where the complement of the orbit is a divisor

Advancement in the study of automorphism groups of affine varieties

Abstract

We construct examples of normal affine varieties X of dimension greater than or equal to 4 such that the group of special automorphisms SAut(X) acts on X with an open orbit O and the complement X\O has codimension one.