Characteristic classes and stability conditions for projective Kleinian orbisurfaces

Bronson Lim; Franco Rota

Characteristic classes and stability conditions for projective Kleinian orbisurfaces

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arxiv 2001.09139 v2 pith:NO3LK5ST submitted 2020-01-24 math.AG

Bronson Lim , Franco Rota This is my paper · ORCID

classification math.AG

keywords bridgelandconditionsconstructionkleiniansingularitiessmoothstabilitysurfaces

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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 To\"en-Hirzebruch-Riemann-Roch theorem.

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Moduli spaces on the Kuznetsov component of Fano threefolds of index 2
math.AG 2019-08 conditional novelty 6.0 of 10

For general quartic double solids, two varieties are isomorphic if and only if their Kuznetsov components are equivalent, without assuming the equivalence has Fourier-Mumford type.

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