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Bridgeland Stability conditions on threefolds I: Bogomolov-Gieseker type inequalities

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arxiv 1103.5010 v2 pith:QOPTEKHS submitted 2011-03-25 math.AG

Arend Bayer , Emanuele Macri , Yukinobu Toda This is my paper · ORCID
classification math.AG
keywords bogomolov-giesekerconjectureinequalitybridgelandcharactercherncomplexesconditions
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We construct new t-structures on the derived category of coherent sheaves on smooth projective threefolds. We conjecture that they give Bridgeland stability conditions near the large volume limit. We show that this conjecture is equivalent to a Bogomolov-Gieseker type inequality for the third Chern character of certain stable complexes. We also conjecture a stronger inequality, and prove it in the case of projective space, and for various examples. Finally, we prove a version of the classical Bogomolov-Gieseker inequality, not involving the third Chern character, for stable complexes.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The finite degree formula for normalized volumes

    math.AG 2026-07 accept novelty 8.0 of 10

    For finite crepant morphisms of klt singularities, normalized volume scales exactly by the degree of the morphism.

  2. Proper moduli spaces of orthosymplectic complexes

    math.AG 2025-12 conditional novelty 7.0 of 10

    Semistable orthosymplectic complexes on smooth projective varieties admit proper good moduli spaces, giving a new compactification for O_n and Sp_{2n} principal bundle moduli.

  3. A Real Reduction of the Manifold of Bridgeland Stability Conditions

    math.AG 2025-06 accept novelty 7.0 of 10

    A quotient of the stability manifold by an equivalence relation is a real manifold of half dimension, and the original manifold can be reconstructed from the quotient together with the relation ≲.

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