On motivic Donaldson-Thomas invariants on the local projective plane

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 .

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2019

Author dc:creator

• Shi, Yun

Contributors dc:contributor

• Katz, Sheldon
• Nevins, Thomas
• Bradlow, Steven
• Haboush, William

• motivic DT theory, local projective plane

Statement dc:rights

• Copyright 2019 Yun Shi

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/105891

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/105891