Fourier-Mukai transforms and stable sheaves on Weierstrass elliptic surfaces

2019/10/06 by Wanmin Liu, Liu, Wanmin, Jason Lo +3
Mathematics · #14J27 (Primary) 14J33 #14J60 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1910.02477

openalex publication_date 2019/10/06 · openalex created_date 2019/10/10 · openalex updated_date 2026/07/28

Abstract

On a Weierstraß elliptic surface X, we define a `limit' of Bridgeland stability conditions, denoted as Z^l-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 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. 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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