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arXiv · 2105.12621

The geometry of polynomial representations

Arthur Bik·Jan Draisma·Rob H. Eggermont·Andrew Snowden
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Abstract

We define a GL-variety 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 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.

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Arthur Bik, Jan Draisma, Rob H. Eggermont, Andrew Snowden. 2021-05-26. The geometry of polynomial representations. https://doi.org/10.1093/imrn%2Frnac220

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