English

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 KK, we construct a standard monomial basis for the arc space of the determinantal variety over KK. As an application, we prove the arc space analogue of the first and second fundamental theorems of invariant theory for the general linear group.

Keywords

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