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arXiv · 1705.04011

Stability conditions, Bogomolov-Gieseker type inequalities and Fano 3-folds

Dulip Piyaratne
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Abstract

We develop a framework to modify the Bogomolov-Gieseker type inequality conjecture introduced by Bayer-Macri-Toda, in order to construct a family of geometric Bridgeland stability conditions on any smooth projective 3-fold. We show that it is enough to check these modified inequalities on a small class of tilt stable objects. We extend some of the techniques in the works by Li and Bernardara-Macri-Schmidt-Zhao to formulate a strong form of Bogomolov-Gieseker inequality for tilt stable objects on Fano 3-folds. Consequently, we establish our modified Bogomolov-Gieseker type inequality conjecture for general Fano 3-folds, including an optimal inequality for the blow-up of $P^3$ at a point.

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Dulip Piyaratne. 2017-05-11. Stability conditions, Bogomolov-Gieseker type inequalities and Fano 3-folds. https://arxiv.org/abs/1705.04011

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