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Counting invariant of perverse coherent sheaves and its wall-crossing

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arxiv 0809.2992 v5 pith:GF32XJYG submitted 2008-09-17 math.AG hep-th

Kentaro Nagao , Hiraku Nakajima This is my paper · ORCID
classification math.AGhep-th
keywords invariantscalabi-yauchamberschoicescoherentcountingdonaldson-thomasperverse
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We introduce moduli spaces of stable perverse coherent systems on small crepant resolutions of Calabi-Yau 3-folds and consider their Donaldson-Thomas type counting invariants. The stability depends on the choice of a component (= a chamber) in the complement of finitely many lines (= walls) in the plane. We determine all walls and compute generating functions of invariants for all choices of chambers when the Calabi-Yau is the resolved conifold. For suitable choices of chambers, our invariants are specialized to Donaldson-Thomas, Pandharipande-Thomas and Szendroi invariants.

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