2022/06/21 by Hao Sun, Sun, Hao Max
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2206.10392
openalex publication_date 2022/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.