Real Torus Actions on Real Affine Algebraic Varieties

TL;DR

This paper extends the Altmann-Hausen framework for describing normal affine algebraic varieties with torus actions to the real case, simplifying the presentation for quasi-split real tori.

Contribution

It generalizes the Altmann-Hausen presentation to real algebraic varieties and introduces a simplified approach for quasi-split real tori.

Findings

Extended the Altmann-Hausen presentation to real varieties.

Provided a simpler description for quasi-split real tori.

Enhanced understanding of real algebraic torus actions.

Abstract

We extend the Altmann-Hausen presentation of normal affine algebraic C-varieties endowed with effective torus actions to the real setting. In particular, we focus on actions of quasi-split real tori, in which case we obtain a simpler presentation.