# 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…

## 6 Citations

### Characteristic classes and stability conditions for projective Kleinian orbisurfaces

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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…

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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…

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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

- MathematicsJournal of Pure and Applied Algebra
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### Characteristic classes and stability conditions for projective Kleinian orbisurfaces

- MathematicsMathematische Zeitschrift
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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…

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