The very good property for moduli of parabolic bundles and the Deligne-Simpson problem Public Deposited

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  • March 22, 2019
Creator
  • Soibelman, Alexander
    • Affiliation: College of Arts and Sciences, Department of Mathematics
Abstract
  • In Quantization of Hitchin's Integrable System and Hecke Eigensheaves, Beilinson and Drinfeld introduced the very good property for a smooth complex equidimensional stack. They prove that for a semisimple complex group G, the moduli stack of G-bundles over a smooth complex projective curve X is very good, as long as X has genus g > 1. In the case of the projective line, when g = 0, this is not the case. However, the result can sometimes be extended to the projective line by introducing additional parabolic structure at a collection of marked points and slightly modifying the definition of a very good stack. We provide a sufficient condition for the moduli stack of parabolic vector bundles over the complex projective line to be very good. We then use this property to study the space of solutions to the Deligne-Simpson problem.
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  • In Copyright
Advisor
  • Arinkin, Dmitry
Degree
  • Doctor of Philosophy
Graduation year
  • 2014
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