FourierMukai transforms of slope stable torsionfree sheaves and stable 1dimensional 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. In the first half of this article, we define the notion of limit tilt stability, which is closely related to Bayer's polynomial stability. We 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 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. In the second half of this article, we define a limit stability for complexes that vanish on the generic fiber of the fibration. We show that onedimensional stable sheaves with positive twisted third Chern character correspond to such limit stable complexes under a FourierMukai transform. When the elliptic fibration has a numerically $K$trivial base, we show that these limit stable complexes are the stable objects with respect to a Bridgeland stability on a triangulated subcategory of the derived category of coherent sheaves on the threefold.
 Publication:

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

 Mathematics  Algebraic Geometry;
 14J30 (Primary) 14J33;
 14J60 (Secondary)
 EPrint:
 54 pages