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Projectivity and
effective global generation of determinantal line bundles on
quiver moduli
Pieter Belmans, Chiara Damiolini, Hans Franzen, Victoria Hoskins, Svetlana Makarova and Tuomas Tajakka |
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Vol. 20 (2026), No. 4, 747–800
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Abstract |
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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 and 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. |
Keywords
good moduli space, moduli stack, moduli of quiver
representations
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Mathematical Subject Classification
Primary: 14D23, 16G20
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Milestones
Received: 10 October 2022
Revised: 31 January 2025
Accepted: 2 April 2025
Published: 30 April 2026
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Authors |
| Pieter Belmans | |
| Mathematical Institute Utrecht University Utrecht Netherlands |
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| Chiara Damiolini | |
| Department of Mathematics University of Texas at Austin Austin, TX United States |
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| Hans Franzen | |
| Institute of Mathematics Paderborn University Paderborn Germany |
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| Victoria Hoskins | |
| Fakultät für Mathematik Universität Duisburg-Essen Essen Germany |
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| Svetlana Makarova | |
| Mathematical Sciences
Institute Australian National University Canberra, ACT Australia |
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| Tuomas Tajakka | |
| Department of Mathematics Stockholm University Stockholm Sweden |
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| © 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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