Counting invariant of perverse coherent sheaves and its wall-crossing

Details Counting invariant of perverse coherent sheaves and its wall-crossing Counting invariant of perverse coherent sheaves and its wall-crossing

2008-09-17

arxiv.org/abs/0809.2992v5

Mathematics

Algebraic Geometry

42 pages, 12 figures; subsection 4.6 is modified, some minor changes; to appear in IMRN

Scientific paper

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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