Seminar Algebra and Geometry: Nathan Ilten (Max Planck Institute)

Upgrades and Downgrades of p-divisors

A p-divisor on a normal variety Y is a divisor satisfying some positivity properties, where the usual integral or rational coefficients have been replaced by polyhedral coeffi- cients. K. Altmann and J. Hausen have shown that there is a correspondence between p-divisors and affine T-varieties, i.e. normal varieties together with some effective torus action. Given some T-variety X, one can try to ”upgrade” the torus action by considering some larger torus acting on X, or ”downgrade” the torus action by considering the action of some subtorus. I will discuss how these upgrading and downgrading procedures change the corresponding p-divisors. Time permitting, I will present an application of the upgrade procedure dealing with the p-divisors of Cox rings of certain T-varieties. This is joint work with R. Vollmert.

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