Algebraic vector bundles on the 2-sphere and smooth rational varieties with infinitely many real forms

TL;DR

This paper constructs smooth rational real algebraic varieties in dimensions four and higher that have infinitely many distinct real forms, advancing understanding of real algebraic geometry.

Contribution

It introduces a method to produce high-dimensional rational varieties with infinitely many non-isomorphic real forms, a novel result in the field.

Findings

Existence of such varieties in all dimensions ≥ 4

Construction method for varieties with infinitely many real forms

Implications for classification of real algebraic varieties

Abstract

We construct smooth rational real algebraic varieties of every dimension $\ge$ 4 which admit infinitely many pairwise non-isomorphic real forms.