On motivic Donaldson-Thomas invariants on the 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 .