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Computing motivic Donaldson-Thomas invariants

University of British Columbia

This thesis develops a method (dimensional reduction) to compute motivic Donaldson--Thomas invariants. The method is then employed to compute these invariants in several different cases. Given a moduli scheme with a symmetric obstruction theory a Donaldson--Thomas type invariant can be defined by integrating Behrend's function over the scheme. Motivic Donaldson--Thomas theory aims to provide a more refined invariant associated to each such moduli space - a virtual motive. From the modern point of view motivic Donaldson-Thomas invariants should be defined for a three dimensional Calabi--Yau category. These categories often arise in a geometric context as the derived category of representations of a quiver with potential. Provided the potential has a linear factor we are able to reduce the problem of computing the corresponding virtual motives to a much simpler one. This includes geometric examples coming from local curves which we compute explicitly.

Text

2012-04-10

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/41935

Mathematics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/