Representation Theory and Vector Bundles

Abstract

In this paper, we solve two geometrically-motivated problems concerning vector bundles over projective varieties by using techniques from ordinary representation theory, modular representation theory, and combinatorics. We prove that (1) the k-th Chern character class of a vector bundle E over a smooth projective variety can be written as a rational combination of the k-th Chern classes of the family of vector bundles E⊕s ; and (2) every ample vector bundle has a globally generated tensor power in arbitrary characteristic.