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

Arend Bayer, Emanuele Macri, Yukinobu Toda

Number 8
Author Dr. Emanuele Macrì
Year 2011

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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