{
  "id": "1602.02116",
  "version": "v1",
  "published": "2016-02-05T18:27:16.000Z",
  "updated": "2016-02-05T18:27:16.000Z",
  "title": "A note on the subadditivity of Syzygies",
  "authors": [
    "Sabine El Khoury",
    "Hema Srinivasan"
  ],
  "comment": "4 pages",
  "categories": [
    "math.AC"
  ],
  "abstract": "Let $R=S/I$ be a graded algebra with $t_i$ and $T_i$ being the minimal and maximal shifts in the minimal $S$ resolution of $R$ at degree $i$. In this paper we prove that $t_n\\leq t_1+T_{n-1}$, for all $n$ and as a consequence, we show that for Gorenstein algebras of codimension $h$, the subadditivity of maximal shifts $T_i$ in the minimal resolution holds for $i \\le h-1$, i.e, we show that $T_i \\leq T_a+T_{i-a}$ for $i\\le h-1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-05T18:27:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13D02"
    ],
    "keywords": [
      "subadditivity",
      "maximal shifts",
      "minimal resolution holds",
      "gorenstein algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160202116E"
    }
  }
}