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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 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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Acknowledgements

We wish to thank Aaron Bertram, and Michael Wemyss for many fruitful conversations on this topic. We are grateful to Arend Bayer for discussing Sect. 5 with us.

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Authors and Affiliations

  1. Department of Mathematics, California State University San Bernardino, San Bernardino, CA, 92407, USA

    Bronson Lim

  2. Department of Mathematics, Rutgers University, Piscataway, NJ, 08854, USA

    Franco Rota

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  1. Bronson Lim
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  2. Franco Rota
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Correspondence to Franco Rota.

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The first author was supported by RTG grant #1246989 at the University of Utah.

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Lim, B., Rota, F. Characteristic classes and stability conditions for projective Kleinian orbisurfaces. Math. Z. 300, 827–849 (2022). https://doi.org/10.1007/s00209-021-02805-8

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