Upgrading and Downgrading Torus Actions

Abstract

K. Altmann and J. Hausen have shown that affine T-varieties can be described in terms of p-divisors. Given a p-divisor describing a T-variety X, we show how to construct new p-divisors describing X with respect to actions by larger tori. Conversely, if dim T=dim X-1, we show how to construct new p-divisors describing X with respect to actions by closed subtori of T. As a first application, we give explicit constructions for the p-divisors describing certain Cox rings. Furthermore, we show how to upgrade the p-divisors describing the total spaces of homogeneous deformations of toric varieties.

29 pages, 10 figures

References in corpus (4)

• Polarized Complexity-One T-Varieties
• On Generalized Wronskians
• The Geometry of T-Varieties
• P-Divisors of Cox Rings

Cited by in corpus (6)

• K-Stability for Fano Manifolds with Torus Action of Complexity One
• On Generalized Wronskians
• The Geometry of T-Varieties
• Families of Invariant Divisors on Rational Complexity-One T-Varieties
• On deformations of toric varieties
• Calculating Generators of Multigraded Algebras