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arXiv · 1609.03245

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

Hao Max Sun
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Abstract

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 $\mathbb{P}^3$.

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Hao Max Sun. 2016-09-12. Tilt-stability, vanishing theorems and Bogomolov-Gieseker type inequalities. https://arxiv.org/abs/1609.03245

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