Generalized Bogomolov-Gieseker type inequalities on Fano 3-folds

2016/07/25 by Dulip Piyaratne, Piyaratne, Dulip · 1 citation
Mathematics · #14J45 #14J60 #14K99 #18E10 #18E30 #18E40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Geometric and Algebraic Topology #Primary 14F05 #Secondary 14J30

paper · pdf · doi:10.48550/arxiv.1607.07172

openalex publication_date 2016/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Some remarks on Fano threefolds of index two and stability conditions

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