Simple examples of affine manifolds with infinitely many exotic models

TL;DR

This paper presents a straightforward method to construct affine varieties with infinitely many distinct models, demonstrating that for any dimension greater than one, there exist Stein manifolds with uncountably many affine structures.

Contribution

Introduces a simple general construction method for affine varieties with infinitely many exotic models, expanding understanding of affine manifold structures.

Findings

Existence of Stein manifolds with uncountably many affine structures for all dimensions greater than one.

Construction method applicable to a broad class of affine varieties.

Demonstrates richness of affine structures beyond classical examples.

Abstract

We give a simple general method of construction of affine varieties with infinitely many exotic models. In particular we show that for every d>1 there exists a Stein manifold of dimension d which has uncountably many different structures of affine variety.