Papers › Fourier-Mukai transforms and stable sheaves on Weierstrass elliptic surfaces
Fourier-Mukai transforms and stable sheaves on Weierstrass elliptic surfaces
Wanmin Liu, Jason Lo, Cristian Martinez
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On a Weierstra{\ss} elliptic surface X, we define a `limit' of Bridgeland stability conditions, denoted as Zˡ-stability, by moving the polarisation towards the fiber direction in the ample cone while keeping the volume of the polarisation fixed. We describe conditions under which a slope stable torsion-free sheaf is taken by a Fourier-Mukai transform to a Zˡ-stable object, and describe a modification upon which a Zˡ-semistable object is taken by the inverse Fourier-Mukai transform to a slope semistable torsion-free sheaf. We also study wall-crossing for Bridgeland stability, and show that 1-dimensional twisted Gieseker semistable sheaves are taken by a Fourier-Mukai transform to Bridgeland semistable objects.
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