Inversion maps and torus actions on rational homogeneous varieties

TL;DR

This paper explores the geometric structure of birational transformations linked to rational homogeneous varieties with specific $ ext{C}^*$-actions, enhancing understanding of their symmetries and transformations.

Contribution

It provides a geometric description of birational transformations associated with rational homogeneous varieties under $ ext{C}^*$-actions with no proper isotropy subgroups.

Findings

Characterization of birational transformations via inversion maps

Description of torus actions on rational homogeneous varieties

Insights into the geometric structure of varieties with $ ext{C}^*$-actions

Abstract

Complex projective algebraic varieties with $\mathbb{C}^*$-actions can be thought of as geometric counterparts of birational transformations. In this paper we describe geometrically the birational transformations associated to rational homogeneous varieties endowed with a $\mathbb{C}^*$-action with no proper isotropy subgroups.