Tilt-stability, vanishing theorems and Bogomolov-Gieseker type inequalities

摘要

We investigate the tilt-stability of stable sheaves on projective varieties with respect to certain tilt-stability conditions depends on two parameters constructed by Bridgeland [11] (see also [1,6,5]). For a stable sheaf, we give effective bounds of these parameters such that the stable sheaf is tilt-stable. These allow us to prove new vanishing theorems for stable sheaves and an effective Serre vanishing theorem for torsion free sheaves. Using these results, we also prove Bogomolov-Gieseker type inequalities for the third Chern character of a stable sheaf on P-3. (C) 2019 Elsevier Inc. All rights reserved.