On motivic Donaldson-Thomas invariants on the local projective plane
Shi, Yun
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https://hdl.handle.net/2142/105891
Description
Title
On motivic Donaldson-Thomas invariants on the local projective plane
Author(s)
Shi, Yun
Issue Date
2019-07-03
Director of Research (if dissertation) or Advisor (if thesis)
Katz, Sheldon
Doctoral Committee Chair(s)
Nevins, Thomas
Committee Member(s)
Bradlow, Steven
Haboush, William
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
motivic DT theory, local projective plane
Abstract
Motivic Donaldson-Thomas (DT) invariant is a categorification of the classical DT invariant which contains more information of the local structure of a moduli space. In this thesis, we give three (partial) studies on the motivic DT invariants for various moduli spaces associated to the local projective plane (ωP2). In the first project, we give a construction of an orientation data for the stack of coherent sheaves on ωP2. In the second project, we construct a d-critical locus structure on Hilbn(ωP2), which is useful for recovering the computation of the motivic DT invariant associated to Hilbn(ωP2). Finally, we give some explicit computations on the motivic DT invariants associated to the stack of quiver representations, for a quiver related to ωP2 .
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