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Fourier-Mukai transforms of slope stable torsion-free sheaves and stable 1-dimensional sheaves on Weierstrass elliptic threefolds. (arXiv:1710.03771v1 [math.AG])
来源于:arXiv
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
Fourier-Mukai transform of a slope stable torsion-free sheaf satisfying a
vanishing condition in codimension 2 (e.g. a reflexive sheaf) is a limit stable
object. We also show that the inverse Fourier-Mukai transform of a limit tilt
semistable object of nonzero fiber degree is a slope semistable torsion-free
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 one-dimensional
stable sheaves with positive twisted third Chern character correspond to such
limit stable complexes under a Fourier-Mukai transform. When the elliptic
fibration has a numerically $ 查看全文>>