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

Let \(X\) be a smooth complex projective variety. In 2002, Bridgeland defined a notion of stability for the objects in \(D^b(X)\), the bounded derived category of coherent sheaves on \(X\), which generalized the notion of slope stability for vector bundles on curves. There are many nice connections...

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Bibliographic Details
Published inarXiv.org
Main Authors Tramel, Rebecca, Xia, Bingyu
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 27.08.2018
Subjects
Economic models
Geometry
Sheaves
Slope stability
Surface stability
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Summary:Let \(X\) be a smooth complex projective variety. In 2002, Bridgeland defined a notion of stability for the objects in \(D^b(X)\), the bounded derived category of coherent sheaves on \(X\), which generalized 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 \({\rm Stab}(X)\), the stability manifold of \(X\). We then construct the moduli space \(M_{\sigma}(\mathcal{O}_X)\) of \(\sigma\)-semistable objects of class \([\mathcal{O}_X]\) in \(K_0(X)\) after wall-crossing.
ISSN:2331-8422