Bik, Arthur; Draisma, Jan; Eggermont, Rob H.; Snowden, Andrew (2022). The Geometry of Polynomial Representations. International Mathematics Research Notices, 2023(16), pp. 14131-14195. Oxford University Press 10.1093/imrn/rnac220
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We define a GL-variety to be an (typically infinite dimensional) algebraic variety equipped with an action of the infinite general linear group under which the coordinate ring forms a polynomial representation. Such varieties have been used to study asymptotic properties of invariants like strength and tensor rank and played a key role in two recent proofs of Stillman’s conjecture. We initiate a systematic study of GL -varieties and establish a number of foundational results about them. For example, we prove a version of Chevalley’s theorem on constructible sets in this setting.
Item Type: |
Journal Article (Original Article) |
|---|---|
Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Bik, Michel Arthur, Draisma, Jan |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
1073-7928 |
Publisher: |
Oxford University Press |
Language: |
English |
Submitter: |
Zarif Ibragimov |
Date Deposited: |
14 Mar 2023 09:40 |
Last Modified: |
03 Sep 2023 02:46 |
Publisher DOI: |
10.1093/imrn/rnac220 |
ArXiv ID: |
2105.12621v2 |
BORIS DOI: |
10.48350/179979 |
URI: |
https://boris.unibe.ch/id/eprint/179979 |
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