Forms of almost homogeneous varieties over perfect fields

Abstract

We study the k-forms of almost homogeneous varieties over perfect base fields k. First, we discuss criteria for the existence of k-forms in the homogeneous case. Then, we extend the Luna-Vust theory from algebraically closed fields to perfect fields to determine when a given k-form of the open orbit of an almost homogeneous variety extends to a k-form of the entire variety. Finally, in the last section, we apply these results to determine the real forms of complex almost homogeneous SL(2)-threefolds.

46 pages, final version, to appear in Annales Henri Lebesgue

References in corpus (3)

• Real Torus Actions on Real Affine Algebraic Varieties
• Torus actions on affine varieties over characteristic zero fields
• Real forms of minimal SL${}_2$-threefolds

Cited by in corpus (1)

• Real structures on nilpotent orbit closures