
Bridgeland stability conditions on threefolds I: Bogomolov-Gieseker type inequalities
Author(s) -
Arend Bayer,
Emanuele Macrì,
Yukinobu Toda
Publication year - 2013
Publication title -
journal of algebraic geometry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.824
H-Index - 50
eISSN - 1534-7486
pISSN - 1056-3911
DOI - 10.1090/s1056-3911-2013-00617-7
Subject(s) - mathematics , conjecture , pure mathematics , character (mathematics) , type (biology) , limit (mathematics) , space (punctuation) , stability (learning theory) , derived category , inequality , coherent sheaf , mathematical analysis , geometry , linguistics , computer science , ecology , philosophy , machine learning , biology , functor
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.