Yash Singh, University of Waterloo
Vector bundles on toric stacks
This thesis is concerned with a generalization of Klyachko's classification of toric vector bundles to toric stacks.The work of Klyachko gave an elegant method of studying toric vector bundles through filtrations of a vectorspace. We extend these techniques to vector bundles on a toric stack and generalize the aspects of Klyachko'swork to a more geometric setting. In particular, we show that the category of reflexive sheaves on a toric stack isequivalent to a category of filtered reflexives sheaves of its largest Deligne-Mumford substack. We then combinethis with an equivariant version of Gubeladze's result on the splitting of vector bundles on toric varieties to provea classification theorem for vector bundles on toric stacks.
MC 5403