Bridgeland stability conditions on surfaces with curves of negative self-intersection

@article{Tramel2022BridgelandSC,
  title={Bridgeland stability conditions on surfaces with curves of negative self-intersection},
  author={Rebecca Tramel and Bingyu Xia},
  journal={Advances in Geometry},
  year={2022},
  volume={22},
  pages={383 - 408}
}
Abstract Let X be a smooth complex projective variety. In 2002, Bridgeland [6] defined a notion of stability for the objects in 𝔇b(X), the bounded derived category of coherent sheaves on X, which generalised the notion of slope stability for vector bundles on curves. There are many nice connections between stability conditions on X and the geometry of the variety. We construct new stability conditions for surfaces containing a curve C whose self-intersection is negative. We show that these… 

Characteristic classes and stability conditions for projective Kleinian orbisurfaces

We construct Bridgeland stability conditions on the derived category of smooth quasi-projective Deligne–Mumford surfaces whose coarse moduli spaces have ADE singularities. This unifies the

Geometric stability conditions under autoequivalences and applications: Elliptic Surfaces

A BSTRACT . On a Weierstraß elliptic surface, we describe the action of the relative Fourier-Mukai trans- form on the geometric chamber of Stab( X ) , and in the K3 case we also study the action on

The stability manifold of local orbifold elliptic quotients

  • Franco Rota
  • Mathematics
    Journal of the London Mathematical Society
  • 2022
We study the stability manifold of local models of orbifold quotients of elliptic curves. In particular, we show that a region of the stability manifold is a covering space of the regular set of the

An interesting wall-crossing: Failure of the wall-crossing/MMP correspondence.

We show that the wall-crossing in Bridgeland stability fails to be detected by the birational geometry of stable sheaves, and vice versa. There is a wall in the stability space of canonical genus

A note on the Kuznetsov component of the Veronese double cone

Characteristic classes and stability conditions for projective Kleinian orbisurfaces

We construct Bridgeland stability conditions on the derived category of smooth quasi-projective Deligne–Mumford surfaces whose coarse moduli spaces have ADE singularities. This unifies the

References

SHOWING 1-10 OF 22 REFERENCES

The space of stability conditions on the local projective plane

We study the space of stability conditions on the total space of the canonical bundle over the projective plane. We explicitly describe a chamber of geometric stability conditions, and show that its

Lectures on Vector Bundles

Part I. Vector Bundles On Algebraic Curves: 1. Generalities 2. The Riemann-Roch formula 3. Topological 4. The Hilbert scheme 5. Semi-stability 6. Invariant geometry 7. The construction of M(r,d) 8.

Stability conditions on triangulated categories

This paper introduces the notion of a stability condition on a triangulated category. The motivation comes from the study of Dirichlet branes in string theory, and especially from M.R. Douglas's

Moduli of complexes on a proper morphism

Given a proper morphism X -> S, we show that a large class of objects in the derived category of X naturally form an Artin stack locally of finite presentation over S. This class includes S-flat

The space of stability conditions on abelian threefolds, and on some Calabi-Yau threefolds

We describe a connected component of the space of stability conditions on abelian threefolds, and on Calabi-Yau threefolds obtained as (the crepant resolution of) a finite quotient of an abelian

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

La singularité de O’Grady

Let M be the moduli space of semistable sheaves with Mukai vector 2v on an abelian or K3 surface where v is primitive such that =2. We show that the blow-up of the reduced singular locus of M

Stability conditions and extremal contractions

We study extremal contractions from smooth projective varieties via a moduli theoretic approach. In the two dimensional case, we show that any extremal contraction appears as a moduli space of

Singular symplectic moduli spaces

Moduli spaces of semistable sheaves on a K3 or abelian surface with respect to a general ample divisor are shown to be locally factorial, with the exception of symmetric products of a K3 or abelian