2017/05/11 by Dulip Piyaratne, Piyaratne, Dulip
Mathematics · Social Sciences · #14F05 (Primary) #14J30 #14J45 #14J60 #14K99 #18E10 #18E30 #18E40 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algorithm #Artificial intelligence #Class (philosophy) #Combinatorics #Computer science #Cone (formal languages) #Conjecture #FOS: Mathematics #Fano plane #Geometric and Algebraic Topology #Geometry and complex manifolds #Inequality #Mathematical analysis #Mathematics #Pure mathematics #Stability (learning theory) #Type (biology) #Vietnamese History and Culture Studies #math.AG #msc:14F05 #msc:14J30 #msc:14J45 #msc:14J60 #msc:14K99 #msc:18E10 #msc:18E30 #msc:18E40
paper · pdf · doi:10.48550/arxiv.1705.04011
41 pages. 6 figures. Comments welcome. This paper supersedes and incorporates many results from the author's unpublished work arXiv:1607.07172v2. arXiv admin note: substantial text overlap with arXiv:1607.07172
arxiv created 2017/05/11 · openalex publication_date 2017/05/11 · arxiv updated 2017/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 P3 at a point.