Affine Non‐Reductive GIT and moduli of representations of quivers with multiplicities
We give an explicit approach to quotienting affine varieties by linear actions of linear algebraic groups with graded unipotent radical, using results from projective Non‐Reductive GIT. Our quotients come with explicit projective completions, whose boundaries we interpret in terms of the original ac...
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| Published in | Journal of the London Mathematical Society Vol. 111; no. 3 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
01.03.2025
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| Online Access | Get full text |
| ISSN | 0024-6107 1469-7750 1469-7750 |
| DOI | 10.1112/jlms.70099 |
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| Abstract | We give an explicit approach to quotienting affine varieties by linear actions of linear algebraic groups with graded unipotent radical, using results from projective Non‐Reductive GIT. Our quotients come with explicit projective completions, whose boundaries we interpret in terms of the original action. As an application, we construct moduli spaces of semistable representations of quivers with multiplicities subject to certain conditions, which always hold in the toric case for a generic stability condition. |
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| AbstractList | We give an explicit approach to quotienting affine varieties by linear actions of linear algebraic groups with graded unipotent radical, using results from projective Non‐Reductive GIT. Our quotients come with explicit projective completions, whose boundaries we interpret in terms of the original action. As an application, we construct moduli spaces of semistable representations of quivers with multiplicities subject to certain conditions, which always hold in the toric case for a generic stability condition. |
| Author | Jackson, Joshua Hoskins, Victoria Hamilton, Eloise |
| Author_xml | – sequence: 1 givenname: Eloise surname: Hamilton fullname: Hamilton, Eloise organization: Newnham College – sequence: 2 givenname: Victoria surname: Hoskins fullname: Hoskins, Victoria organization: Radboud University, IMAPP – sequence: 3 givenname: Joshua orcidid: 0000-0003-1820-9016 surname: Jackson fullname: Jackson, Joshua email: jjj26@cam.ac.uk organization: St John's College |
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| Copyright | 2025 The Author(s). is copyright © London Mathematical Society. |
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| Title | Affine Non‐Reductive GIT and moduli of representations of quivers with multiplicities |
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