Fourier-Mukai transforms of slope stable torsion-free sheaves on Weierstrass elliptic surfaces

2017/10/12 by Jason Lo, Lo, Jason
Mathematics · #14J27 (Primary) 14J33 #14J60 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1710.04652

openalex publication_date 2017/10/12 · openalex created_date 2017/11/10 · openalex updated_date 2026/07/28

Abstract

On a Weierstraß elliptic surface X, we define a `limit' of Bridgeland stability conditions, denoted Z^l-stability, by varying the polarisation in the definition of Bridgeland stability along a curve in the ample cone of X. 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 on D^b(X) to a Z^l-stable object, while a Z^l-semistable object of nonzero fiber degree can be modified so that its inverse Fourier-Mukai transform is a slope semistable torsion-free sheaf.

Citations

• Hall algebras in the derived category and higher rank DT invariants

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