{
  "id": "1802.07203",
  "version": "v1",
  "published": "2018-02-20T17:06:03.000Z",
  "updated": "2018-02-20T17:06:03.000Z",
  "title": "Endomorphisms of Koszul complexes: formality and application to deformation theory",
  "authors": [
    "Francesca Carocci",
    "Marco Manetti"
  ],
  "categories": [
    "math.AG",
    "math.QA"
  ],
  "abstract": "We study the differential graded Lie algebra of endomorphisms of the Koszul resolution of a regular sequence on a unitary commutative $\\K$-algebra $R$ and we prove that it is homotopy abelian over $\\K$, while it is generally not formal over $R$. We apply this result to prove an annihilation theorem for obstructions of (derived) deformations of locally complete intersection ideal sheaves on projective schemes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-20T17:06:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B70",
      "14D15",
      "18G50",
      "13D10"
    ],
    "keywords": [
      "deformation theory",
      "koszul complexes",
      "endomorphisms",
      "locally complete intersection ideal sheaves",
      "application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}