Wanmin Liu: Fourier–Mukai transforms of slope stable torsion-free sheaves on Weierstrass elliptic surfaces
Time: Wed 2019-05-15 13.15
Lecturer: Wanmin Liu (Uppsala)
Location: Room 306, House 6, Kräftriket, Department of Mathematics, Stockholm University
On a Weierstrass elliptic surface X, we define a 'limit' of Bridgeland stability conditions, denoted as Zl-stability, by varying the polarisation along a curve in the ample cone. We show that a slope stable torsion-free sheaf of positive (twisted) degree or a slope stable locally free sheaf is taken by a Fourier–Mukai transform to a Zl-stable object, while a Zl-semistable object of nonzero fiber degree can be modified so that its inverse Fourier–Mukai transform is a slope semistable torsion-free sheaf. As an application, on a Weierstrass elliptic surface of Picard rank two with a negative section, we show that a line bundle of fiber degree at least 2 is taken by the inverse Fourier–Mukai transform to a slope semistable locally free sheaf.