Communications in Analysis and Geometry

Volume 24 (2016)

Number 5

Stability and Fourier–Mukai transforms on higher dimensional elliptic fibrations

Pages: 1047 – 1084



Wu-yen Chuang (Department of Mathematics, National Taiwan University, Taipei, Taiwan)

Jason Lo (Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Il., U.S.A.)


We consider elliptic fibrations with arbitrary base dimensions, and generalise most of the results in [Lo1, Lo2, Lo5]. In particular, we check universal closedness for the moduli of semistable objects with respect to a polynomial stability that reduces to PT-stability on threefolds. We also show openness of this polynomial stability. On the other hand, we write down a criterion under which certain 2-term polynomial semistable complexes are mapped to torsion-free semistable sheaves under a Fourier–Mukai transform. As an application, we construct an open immersion from a moduli of complexes to a moduli of Gieseker stable sheaves on higher dimensional elliptic fibrations.


elliptic fibrations, stability, moduli, Fourier–Mukai transforms

2010 Mathematics Subject Classification

Primary 14J60. Secondary 14J27, 14J30.

Published 6 March 2017