Inversion maps and torus actions on rational homogeneous varieties

Abstract

Complex projective algebraic varieties with ${\mathbb{C}}^{\ast }$-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 ${\mathbb{C}}^{\ast }$-action with no proper isotropy subgroups.