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arXiv · 2206.10392

Bogomolov-Gieseker type inequalities on ruled threefolds

Hao Max Sun
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Abstract

We strengthen a conjecture by the author. This conjecture is a Bogomolov-Gieseker type inequality involving the third Chern character of mixed tilt-stable complexes on fibred threefolds. We extend it from complexes of mixed tilt-slope zero to arbitrary relative tilt-slope. We show that this stronger conjecture implies the support property of Bridgeland stability conditions, and the existence of explicit stability conditions. We prove our conjecture for ruled threefolds, hence improving a previous result by the author.

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Hao Max Sun. 2022-06-21. Bogomolov-Gieseker type inequalities on ruled threefolds. https://arxiv.org/abs/2206.10392

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