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}
}
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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References

SHOWING 1-10 OF 36 REFERENCES

Derived categories of small toric Calabi-Yau 3-folds and counting invariants

We first construct a derived equivalence between a small crepant resolution of an affine toric Calabi-Yau 3-fold and a certain quiver with a superpotential. Under this derived equivalence we

Perverse coherent sheaves on blow-up. I. a quiver description

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

Hilbert schemes and stable pairs: GIT and derived category wall crossings

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

Perverse coherent sheaves on blow-up. II. Wall-crossing and Betti numbers formula

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

Wall crossing in local Calabi Yau manifolds

We study the BPS states of a D6-brane wrapping the conifold and bound to collections of D2 and D0 branes. We find that in addition to the complexified Kahler parameter of the rigid sphere it is

Perverse coherent sheaves and Fourier–Mukai transforms on surfaces, I

We study perverse coherent sheaves on the resolution of rational double points. As examples, we consider rational double points on 2-dimensional moduli spaces of stable sheaves on K3 and elliptic

Donaldson-Thomas invariants via microlocal geometry

We prove that Donaldson-Thomas type invariants are equal to weighted Euler characteristics of their moduli spaces. In particular, such invariants depend only on the scheme structure of the moduli

Super-rigid Donaldson-Thomas Invariants

We solve the part of the Donaldson-Thomas theory of Calabi-Yau threefolds which comes from super-rigid rational curves. As an application, we prove a version of the conjectural

Stability structures, motivic Donaldson-Thomas invariants and cluster transformations

We define new invariants of 3d Calabi-Yau categories endowed with a stability structure. Intuitively, they count the number of semistable objects with fixed class in the K-theory of the category

Non-commutative Donaldson–Thomas invariants and the conifold

Given a quiver algebra A with relations defined by a superpotential, this paper defines a set of invariants of A counting framed cyclic A–modules, analogous to rank–1 Donaldson–Thomas invariants of