{
  "id": "2108.06864",
  "version": "v1",
  "published": "2021-08-16T02:42:21.000Z",
  "updated": "2021-08-16T02:42:21.000Z",
  "title": "Standard monomials and invariant theory for arc spaces I: general linear group",
  "authors": [
    "Andrew R. Linshaw",
    "Bailin Song"
  ],
  "comment": "40pages",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-16T02:42:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F50",
      "14M12",
      "14L24"
    ],
    "keywords": [
      "general linear group",
      "invariant theory",
      "standard monomial basis",
      "standard monomial theory",
      "arc space analogue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}