# 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

Abstract:

On a Weierstrass elliptic surface *X*, we define a 'limit' of Bridgeland stability conditions, denoted as *Z ^{l}*-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

*Z*-stable object, while a

^{l}*Z*-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.

^{l}