{
  "id": "1510.05832",
  "version": "v1",
  "published": "2015-10-20T10:54:21.000Z",
  "updated": "2015-10-20T10:54:21.000Z",
  "title": "Bloch's conjecture and valences of correspondences for K3 surfaces",
  "authors": [
    "Claudio Pedrini"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Bloch's conjecture for a surface $X$ over an algebraically closed field $k$ states that every homologically trivial correspondence $\\Gamma $ acts as 0 on the Albanese kernel $T(X_{\\Omega})$, where $\\Omega $ is a universal domain containing $k$. Here we prove that, for a complex K3 surface $X$, Bloch's conjecture is equivalent to the existence of a valence for every correspondence. We also give applications of this result to the case of a correspondence associated to an automorphisms of finite order and to the existence of constant cycle curves on $X$. Finally we show that Franchetta's conjecture, as stated by K.O'Grady, holds true for the family of polarized K3 surfacees of genus $g$, if $ 3 \\le g \\le 6$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-20T10:54:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "blochs conjecture",
      "complex k3 surface",
      "constant cycle curves",
      "albanese kernel",
      "universal domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151005832P"
    }
  }
}