Stability and Fourier-Mukai transforms on higher dimensional elliptic fibrations
Journal
Communications in Analysis and Geometry
Journal Volume
24
Journal Issue
5
Pages
1047-1084
Date Issued
2016
Author(s)
Chuang, W.-Y.
Abstract
We consider elliptic fibrations with arbitrary base dimensions, and generalise most of the results in [Lo1, Lo2, Lo5]. In particular, we check universal closedness for the moduli of semistable objects with respect to a polynomial stability that reduces to PT-stability on threefolds. We also show openness of this polynomial stability. On the other hand, we write down a criterion under which certain 2-term polynomial semistable complexes are mapped to torsion-free semistable sheaves under a Fourier-Mukai transform. As an application, we construct an open immersion from a moduli of complexes to a moduli of Gieseker stable sheaves on higher dimensional elliptic fibrations.
SDGs
Type
journal article