{
  "id": "1810.05813",
  "version": "v1",
  "published": "2018-10-13T07:49:09.000Z",
  "updated": "2018-10-13T07:49:09.000Z",
  "title": "The absolutely Koszul and Backelin-Roos properties for spaces of quadrics of small codimension",
  "authors": [
    "Rasoul Ahangari Maleki",
    "Liana M. Şega"
  ],
  "comment": "37 pages",
  "categories": [
    "math.AC"
  ],
  "abstract": "Let $\\kk$ be a field and let $R$ be a standard graded quadratic $\\kk$-algebra with $\\dim_{\\kk}R_2\\le 3$. We construct a graded surjective Golod homomorphism $\\varphi \\colon P\\to R$ such that $P$ is a complete intersection of codimension at most $3$. Furthermore, we show that $R$ is absolutely Koszul (that is, every finitely generated $R$-module has finite linearity defect) if and only if $R$ is Koszul if and only if $R$ is not a trivial fiber extension of a standard graded $\\kk$-algebra with Hilbert series $(1+2t-2t^3)(1-t)^{-1}$. In particular, we recover earlier results on the Koszul property of Backelin, Conca and D'Al\\`i.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-13T07:49:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13D02"
    ],
    "keywords": [
      "absolutely koszul",
      "backelin-roos properties",
      "small codimension",
      "trivial fiber extension",
      "finite linearity defect"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}