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 stability conditions lie on a wall of the geometric chamber of Stab(X), the stability manifold of X.We then construct the moduli space Mσ(ℴX) of σ-semistable objects of class [ℴX] in K0(X) after wall-crossing.
Communicated by: I. Coskun
References
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