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arXiv · 2001.09139

Characteristic classes and stability conditions for projective Kleinian orbisurfaces

Bronson Lim·Franco Rota
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Abstract

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 construction for smooth surfaces and Bridgeland's work on Kleinian singularities. The construction hinges on an orbifold version of the Bogomolov-Gieseker inequality for slope semistable sheaves on the stack, and makes use of the Toën-Hirzebruch-Riemann-Roch theorem.

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Bronson Lim, Franco Rota. 2021-05-23. Characteristic classes and stability conditions for projective Kleinian orbisurfaces. https://doi.org/10.1007/s00209-021-02805-8

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