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Title: Representation Theory and Vector Bundles
Authors: Jager, Conner Perry
Advisors: Fulger, Auriel Mihai
Contributors: Huh, June
Department: Mathematics
Class Year: 2015
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.
Extent: 40 pages
Type of Material: Princeton University Senior Theses
Language: en_US
Appears in Collections:Mathematics, 1934-2016

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