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

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

2011-03-25

arxiv.org/abs/1103.5010v1

Mathematics

Algebraic Geometry

44 pages, 4 figures. Comments are welcome

Scientific paper

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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