2016/09/30 by Hao Max Sun · 1 citation
Mathematics · #math.AG
published as Advances in Math. 347 (2019), 677-707 · published version
arxiv created 2021/04/12 · arxiv updated 2021/04/13
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. 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 ℙ3.