Projectivity and effective global generation of determinantal line bundles on quiver moduli
Abstract
We give a moduli-theoretic treatment of the existence and properties of moduli spaces of semistable quiver representations, avoiding methods from geometric invariant theory. Using the existence criteria of Alper--Halpern-Leistner--Heinloth, we show that for many stability functions, the stack of semistable representations admits an adequate moduli space, and prove that this moduli space is proper over the moduli space of semisimple representations. We construct a natural determinantal line bundle that descends to a semiample line bundle on the moduli space and provide new effective bounds for global generation. For an acyclic quiver, we show that this line bundle is ample, thus giving a modern proof of the fact that the moduli space is projective.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Molecular spectroscopy and chirality
Publication details
- Journal / source
- Algebra & Number Theory
- Publisher
- Mathematical Sciences Publishers
- Volume
- 20
- Issue
- 4
- Pages
- 747–800
- Publication date
- 30 April 2026
- Language
- EN