Stability and Fourier-Mukai transforms on elliptic fibrations

2012/06/19 by Jason Lo, Lo, Jason
Mathematics · #14J27 #14J30 (Secondary) #14J60 (Primary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #math.AG #msc:14J27 #msc:14J30 #msc:14J60

paper · pdf · doi:10.48550/arxiv.1206.4281

27 pages. Minor changes to the exposition. To appear in Adv. Math

openalex publication_date 2012/06/19 · arxiv created 2014/01/17 · arxiv updated 2014/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We systematically develop Bridgeland's and Bridgeland-Maciocia's techniques for studying elliptic fibrations, and identify criteria that ensure 2-term complexes are mapped to torsion-free sheaves under a Fourier-Mukai transform. As an application, we construct an open immersion from a moduli of stable complexes to a moduli of Gieseker stable sheaves on elliptic threefolds. As another application, we give various 1-1 correspondences between fiberwise semistable torsion-free sheaves and codimension-1 sheaves on Weierstrass surfaces.

Citations

• Fourier-Mukai transforms and the wall-crossing behavior for Bridgeland's stability conditions
• Good moduli spaces for Artin stacks

Related

• Stability and Fourier-Mukai Transforms on Higher Dimensional Elliptic Fibrations
• Fourier-Mukai transforms of slope stable torsion-free sheaves on Weierstrass elliptic surfaces
• Fourier-Mukai transforms of slope stable torsion-free sheaves on Weierstrass elliptic threefolds
• Fourier-Mukai transforms and stable sheaves on Weierstrass elliptic surfaces
• Fourier-Mukai transforms for K3 and elliptic fibrations