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arXiv · 1206.4281

Stability and Fourier-Mukai transforms on elliptic fibrations

Jason Lo
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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.

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Jason Lo. 2014-01-17. Stability and Fourier-Mukai transforms on elliptic fibrations. https://arxiv.org/abs/1206.4281

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