A generalized Bogomolov–Gieseker inequality for the three-dimensional projective space

2012/07/20 by Emanuele Macrì · 1 citation
Chemistry · Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic structures and combinatorial models #Complex projective space #Computer science #Inequality #Mathematical analysis #Mathematics #Molecular spectroscopy and chirality #Projective space #Projective test #Pure mathematics #Quaternionic projective space #Space (punctuation) #math.AG #msc:14F05 #msc:14J30 #msc:18E30

paper · pdf · doi:10.2140/ant.2014.8.173

published as Algebra Number Theory 8 (2014) 173-190 · 17 pages, 4 figures

arxiv created 2012/07/20 · openalex publication_date 2014/04/20 · arxiv updated 2016/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A generalized Bogomolov–Gieseker inequality for tilt-stable complexes on a smooth projective threefold was conjectured by Bayer, Toda, and the author. We show that such inequality holds true in general if it holds true when the polarization is sufficiently small. As an application, we prove it for the three-dimensional projective space.

Citations

• Bridgeland's stability and the positive cone of the moduli spaces of stable objects on an abelian surface
• Mini-walls for Bridgeland stability conditions on the derived category of sheaves over surfaces
• Bridgeland Stability conditions on threefolds II: An application to Fujita's conjecture
• Some moduli spaces of Bridgeland's stability conditions
• Projectivity and Birational Geometry of Bridgeland moduli spaces
• Bridgeland's stabilities on abelian surfaces
• Algebraic Geometry

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• t-Structures on elliptic fibrations