Standard monomials and invariant theory for arc spaces I: general linear group

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

We corrected a few typos in Lemma 5.2 and Corollary 5.3 that appear in the published version

References in corpus (6)

• Germs of arcs on singular algebraic varieties and motivic integration
• Jet Schemes of Locally Complete Intersection Canonical Singularities
• Arcs on Determinantal Varieties
• Jet schemes and invariant theory
• Arc spaces and the vertex algebra commutant problem
• The global sections of chiral de Rham complexes on compact Ricci-flat Kähler manifolds II

Cited by in corpus (3)

• Cosets of free field algebras via arc spaces
• Functorial constructions related to double Poisson vertex algebras
• On reduced arc spaces of toric varieties