FourierMukai transforms of slope stable torsionfree sheaves on Weierstrass elliptic threefolds
Abstract
We focus on a class of Weierstrass elliptic threefolds that allows the base of the fibration to be a Fano surface or a numerically $K$trivial surface. We define the notion of limit tilt stability, and show that the FourierMukai transform of a slope stable torsionfree sheaf satisfying a vanishing condition in codimension 2 (e.g. a reflexive sheaf) is a limit tilt stable object. We also show that the inverse FourierMukai transform of a limit tilt semistable object of nonzero fiber degree is a slope semistable torsionfree sheaf, up to modification in codimension 2.
 Publication:

arXiv eprints
 Pub Date:
 October 2017
 arXiv:
 arXiv:1710.03771
 Bibcode:
 2017arXiv171003771L
 Keywords:

 Mathematics  Algebraic Geometry;
 14J30 (Primary) 14J33;
 14J60 (Secondary)
 EPrint:
 33 pages. To appear in J. Algebra. The previous version has been split into two parts, the first of which forms the basis of this version (dealing with transforms of torsionfree sheaves)