The geometry of polynomial representations
Abstract
We define a GLvariety to be a (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 GLvarieties, 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2021
 DOI:
 10.48550/arXiv.2105.12621
 arXiv:
 arXiv:2105.12621
 Bibcode:
 2021arXiv210512621B
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Representation Theory
 EPrint:
 46 pages