Stability and Fourier-Mukai transforms on elliptic fibrations

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.

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

References in corpus (5)

• Bridgeland-Stable Moduli Spaces for K-Trivial Surfaces
• Good moduli spaces for Artin stacks
• Some moduli spaces of Bridgeland's stability conditions
• On some moduli of complexes on K3 surfaces
• Moduli Spaces of Semistable Sheaves on Singular Genus One Curves

Cited by in corpus (2)

• Some examples of tilt-stable objects on threefolds
• Stability and Fourier-Mukai Transforms on Higher Dimensional Elliptic Fibrations