Counting invariant of perverse coherent sheaves and its wall-crossing
Algebraic Geometry
2010-10-05 v5 High Energy Physics - Theory
Abstract
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.
Keywords
Cite
@article{arxiv.0809.2992,
title = {Counting invariant of perverse coherent sheaves and its wall-crossing},
author = {Kentaro Nagao and Hiraku Nakajima},
journal= {arXiv preprint arXiv:0809.2992},
year = {2010}
}
Comments
42 pages, 12 figures; subsection 4.6 is modified, some minor changes; to appear in IMRN