t-Structures on elliptic fibrations

2015/09/10 by Jason Lo
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Elliptic curve #Fibration #Homotopy #Mathematical analysis #Mathematics #Pure mathematics #Torsion (gastropod) #math.AG #msc:14D06 #msc:14F05 #msc:14J27 #msc:14J60

paper · pdf · doi:10.1215/21562261-3664887

published as Kyoto J. Math. 56, no. 4 (2016), 701-735 · 29 pages. To appear in Kyoto J. Math

arxiv created 2015/09/10 · openalex publication_date 2016/11/07 · arxiv updated 2016/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We consider t-structures that naturally arise on elliptic fibrations. By filtering the category of coherent sheaves on an elliptic fibration using the torsion pairs corresponding to these t-structures, we prove results describing equivalences of t-structures under Fourier–Mukai transforms.

Citations

• Vector Bundles over Elliptic Fibrations
• Stability and Fourier-Mukai Transforms on Higher Dimensional Elliptic Fibrations
• A generalized Bogomolov-Gieseker inequality for the smooth quadric threefold
• A generalized Bogomolov–Gieseker inequality for the three-dimensional projective space
• Fourier-Mukai Transforms and Bridgeland Stability Conditions on Abelian Threefolds