Fourier-Mukai transforms and stable sheaves on Weierstrass elliptic surfaces

6 Oct 2019 Wanmin Liu Jason Lo Cristian Martinez

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 describe conditions under which a slope stable torsion-free sheaf is taken by a Fourier-Mukai transform to a $Z^l$-stable object, and describe a modification upon which a $Z^l$-semistable object is taken by the inverse Fourier-Mukai transform to a slope semistable torsion-free sheaf... (read more)

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