Standard monomials and invariant theory for arc spaces I: general linear group
Algebraic Geometry
2024-10-24 v4 Commutative Algebra
Abstract
This is the first in a series of papers on standard monomial theory and invariant theory of arc spaces. For any algebraically closed field , we construct a standard monomial basis for the arc space of the determinantal variety over . As an application, we prove the arc space analogue of the first and second fundamental theorems of invariant theory for the general linear group.
Cite
@article{arxiv.2108.06864,
title = {Standard monomials and invariant theory for arc spaces I: general linear group},
author = {Andrew R. Linshaw and Bailin Song},
journal= {arXiv preprint arXiv:2108.06864},
year = {2024}
}
Comments
We corrected a few typos in Lemma 5.2 and Corollary 5.3 that appear in the published version