Resumen de Upgrading and downgrading torus actions

Nathan Owen Ilten, Robert Vollmert

• 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.