{
  "id": "1512.00835",
  "version": "v1",
  "published": "2015-12-02T20:38:19.000Z",
  "updated": "2015-12-02T20:38:19.000Z",
  "title": "Hodge Theory and Deformations of Affine Cones of Subcanonical Projective Varieties",
  "authors": [
    "Carmelo Di Natale",
    "Enrico Fatighenti",
    "Domenico Fiorenza"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "We investigate the relation between the Hodge theory of a smooth subcanonical $n$-dimensional projective variety $X$ and the deformation theory of the affine cone $A_X$ over $X$. We start by identifying $H^{n-1,1}_{\\mathrm{prim}}(X)$ as a distinguished graded component of the module of first order deformations of $A_X$, and later on we show how to identify the whole primitive cohomology of $X$ as a distinguished graded component of the Hochschild cohomology module of the punctured affine cone over $X$. In the particular case of a projective smooth hypersurface $X$ we recover Griffiths' isomorphism between the primitive cohomology of $X$ and certain distinguished graded components of the Milnor algebra of a polynomial defining $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-02T20:38:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine cone",
      "hodge theory",
      "subcanonical projective varieties",
      "distinguished graded component",
      "primitive cohomology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}