{
  "id": "1805.04050",
  "version": "v1",
  "published": "2018-05-10T16:29:54.000Z",
  "updated": "2018-05-10T16:29:54.000Z",
  "title": "Deformation of exceptional collections",
  "authors": [
    "Xiaowen Hu"
  ],
  "comment": "Comments are welcome",
  "categories": [
    "math.AG",
    "math.KT"
  ],
  "abstract": "We show that in a smooth family of Fano or anti-Fano projective varieties, the existence of full exceptional collection of a fiber preserves in the fibers in a neighborhood. Then we show that the noncommutative deformations of a strong exceptional collection of vector bundles induce the same map on the second Hochschild cohomology as the canonical isomorphism induced by the derived equivalence to the corresponding endomorphism algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-10T16:29:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "deformation",
      "strong exceptional collection",
      "second hochschild cohomology",
      "vector bundles induce",
      "full exceptional collection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}