{
  "id": "1604.07888",
  "version": "v1",
  "published": "2016-04-26T23:15:44.000Z",
  "updated": "2016-04-26T23:15:44.000Z",
  "title": "A-infinity algebras associated with elliptic curves and Eisenstein-Kronecker series",
  "authors": [
    "Alexander Polishchuk"
  ],
  "comment": "19 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We compute the A-infinity structure on the self-Ext algebra of the vector bundle $G$ over an elliptic curve of the form $G=\\bigoplus_{i=1}^r P_i\\oplus \\bigoplus_{j=1}^s L_j$, where $(P_i)$ and $(L_j)$ are line bundles of degrees 0 and 1, respectively. The answer is given in terms of Eisenstein-Kronecker numbers $(e^*_{a,b}(z,w))$. The A-infinity constraints lead to quadratic polynomial identities between these numbers, allowing to express them in terms of few ones. Another byproduct of the calculation is the new representation for $e^*_{a,b}(z,w)$ by rapidly converging series.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-26T23:15:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic curve",
      "a-infinity algebras",
      "eisenstein-kronecker series",
      "quadratic polynomial identities",
      "a-infinity structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160407888P"
    }
  }
}