Motivic Donaldson-Thomas invariants of the conifold and the refined topological vertex

Details Motivic Donaldson-Thomas invariants of the conifold and the refined topological vertex Motivic Donaldson-Thomas invariants of the conifold and the refined topological vertex

2011-07-25

arxiv.org/abs/1107.5017v1

Mathematics

Algebraic Geometry

26 pages

Scientific paper

We compute the motivic Donaldson-Thomas theory of the resolved conifold, in all chambers of the space of stability conditions of the corresponding quiver. The answer is a product formula whose terms depend on the position of the stability vector, generalizing known results for the corresponding numerical invariants. Our formulae imply in particular a motivic form of the DT/PT correspondence for the resolved conifold. The answer for the motivic PT series is in full agreement with the prediction of the refined topological vertex formalism.

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