On orbits of the automorphism group on a complete toric variety

Abstract

Let X be a complete toric variety and Aut(X) be the automorphism group. We give an explit description of Aut(X)-orbits on X. In particular, we show that Aut(X) acts on X transitively if and only if X is a product of projective spaces.

10 pages, 4 figures

References in corpus (1)

• Complete toric varieties with reductive automorphism group

Cited by in corpus (4)

• On the moduli of hypersurfaces in toric orbifolds
• On orbits of the automorphism group on an affine toric variety
• Additive group actions on affine T-varieties of complexity one in arbitrary characteristic
• Equivariant completions of affine spaces