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Sym-Noetherianity for
powers of GL-varieties
Christopher H. Chiu, Alessandro Danelon, Jan Draisma, Rob H. Eggermont and Azhar Farooq |
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Vol. 19 (2025), No. 11, 2091–2118
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DOI: 10.2140/ant.2025.19.2091
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Abstract |
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Much recent literature concerns finiteness properties of infinite-dimensional algebraic varieties equipped with an action of the infinite symmetric group, or of the infinite general linear group. In this paper, we study a common generalisation in which the product of both groups acts on infinite-dimensional spaces, and we show that these spaces are topologically Noetherian with respect to this action. |
Keywords
spaces of tensors, complexity of tensors, stabilisation in
varieties of tensors, infinite-dimensional polynomial
representations, equivariant algebraic geometry,
GL-varieties, Sym-varieties, topological Noetherianity,
Vec-varieties, FI-algebras, asymptotic algebraic geometry,
representation stability
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Mathematical Subject Classification
Primary: 13A50, 14R20
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Milestones
Received: 12 December 2022
Revised: 29 October 2024
Accepted: 5 December 2024
Published: 14 September 2025
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Authors |
| Christopher H. Chiu | |
| Department of Mathematics and
Computer Science Eindhoven University of Technology Eindhoven Netherlands |
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| Alessandro Danelon | |
| Department of Mathematics and
Computer Science Eindhoven University of Technology Eindhoven Netherlands |
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| Jan Draisma | |
| Mathematical Institute University of Bern Bern Switzerland |
Department of Mathematics and
Computer Science Eindhoven University of Technology Eindhoven Netherlands |
| Rob H. Eggermont | |
| Department of Mathematics and
Computer Science Eindhoven University of Technology Eindhoven Netherlands |
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| Azhar Farooq | |
| Department of Mathematics and
Computer Science Eindhoven University of Technology Eindhoven Netherlands |
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| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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