Characteristic classes and stability conditions for projective Kleinian orbisurfaces
arXiv:2001.09139 · doi:10.1007/s00209-021-02805-8
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.
arXiv comment22 pages, comments are welcome! Final version, to appear in Math. Z. Section 5 rewritten, Appendix removed and submitted independently as arXiv:2103.10767
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