Projectivity and effective global generation of determinantal line bundles on quiver moduli
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
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| _version_ | 1866915979824463872 |
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| author | Belmans, Pieter Damiolini, Chiara Franzen, Hans Hoskins, Victoria Makarova, Svetlana Tajakka, Tuomas |
| author_facet | Belmans, Pieter Damiolini, Chiara Franzen, Hans Hoskins, Victoria Makarova, Svetlana Tajakka, Tuomas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_00033 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Projectivity and effective global generation of determinantal line bundles on quiver moduli Belmans, Pieter Damiolini, Chiara Franzen, Hans Hoskins, Victoria Makarova, Svetlana Tajakka, Tuomas Algebraic Geometry Representation Theory 14D23, 16G20 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. |
| title | Projectivity and effective global generation of determinantal line bundles on quiver moduli |
| topic | Algebraic Geometry Representation Theory 14D23, 16G20 |
| url | https://arxiv.org/abs/2210.00033 |