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

@article{Nagao2008CountingIO,
title={Counting invariant of perverse coherent sheaves and its wall-crossing},
author={Kentaro Nagao and Hiraku Nakajima},
journal={arXiv: Algebraic Geometry},
year={2008}
}
• Published 17 September 2008
• Mathematics
• arXiv: Algebraic Geometry
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…
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• Mathematics
• 2008
This is the first of two papers studying moduli spaces of a certain class of coherent sheaves, which we call {\it stable perverse coherent sheaves}, on the blowup of a projective surface. They are
• Mathematics
• 2009
We show that the Hilbert scheme of curves and Le Potier's moduli space of stable pairs with one dimensional support have a common GIT construction. The two spaces correspond to chambers on either
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This is the second of series of papers studyig moduli spaces of a certain class of coherent sheaves, which we call stable perverse coherent sheaves, on the blow-up p: b X → X of a projective surface
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