Weighted projective lines as fine moduli spaces of quiver representations

2014/09/24 by Tarig Abdelgadir, Abdelgadir, Tarig, Kazushi Ueda +1
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1409.7050

openalex publication_date 2014/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe weighted projective lines in the sense of Geigle and Lenzing by a moduli problem on the canonical algebra of Ringel. We then go on to study generators of the derived categories of coherent sheaves on the total spaces of their canonical bundles, and show that they are rarely tilting. We also give a moduli construction for these total spaces for weighted projective lines with three orbifold points.

Related

• General sheaves over weighted projective lines
• Introduction to coherent sheaves on weighted projective lines
• Quiver algebras, weighted projective lines, and the Deligne-Simpson problem
• Connections for weighted projective lines
• Moduli for decorated tuples of sheaves and representation spaces for quivers