Speaker: Milena Hering (UConn)

Title:Cox rings of toric vector bundles

Abstract: It is fairly easy to see that the section ring of a line bundle on a toric variety is finitely generated. It is a natural question whether the same holds for the section ring of the Serre line bundle on the projectivization of a toric vector bundle. In my talk I will explain how to obtain examples of a toric vector bundle such that the Cox ring of its projectivization is a polynomial ring over the Cox ring of the blow up of projective space at a given number of points. In particular, these rings may not be finitely generated, hereby answering our question in the negative. This is joint work with Jose Gonzalez, Sam Payne, and Hendrik Süss.