2013/07/07 by Wu-yen Chuang, Chuang, Wu-yen, Jason Lo +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG
paper · pdf · doi:10.48550/arxiv.1307.1845
26 pages. Minor corrections. To appear in Comm. Anal. Geom
openalex publication_date 2013/07/07 · arxiv created 2015/10/08 · arxiv updated 2015/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider elliptic fibrations with arbitrary base dimensions, and generalise previous work by the second author. 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 criteria 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.