Generalized Bogomolov-Gieseker type inequalities on Fano 3-folds
Algebraic Geometry
2017-05-12 v3
Abstract
We modify the conjectural Bogomolov-Gieseker type inequality introduced by Bayer, Macri and Toda to construct a family of geometric Bridgeland stability conditions on smooth projective 3-folds. We give an equivalent conjecture which needs to check these inequalities for a small class of tilt stable objects. We extend some of the techniques in Li's work for Fano 3-folds of Picard rank one to establish our modified Bogomolov-Gieseker type inequality conjecture for general Fano 3-folds.
Keywords
Cite
@article{arxiv.1607.07172,
title = {Generalized Bogomolov-Gieseker type inequalities on Fano 3-folds},
author = {Dulip Piyaratne},
journal= {arXiv preprint arXiv:1607.07172},
year = {2017}
}
Comments
Withdrawn for now due to an error in Lemma 5.4 which affects essentially the rest of the paper