{
  "id": "math/0607558",
  "version": "v1",
  "published": "2006-07-21T21:37:04.000Z",
  "updated": "2006-07-21T21:37:04.000Z",
  "title": "On the discriminant locus of a Lagrangian fibration",
  "authors": [
    "Justin Sawon"
  ],
  "comment": "17 pages",
  "journal": "Math. Ann. 341 (2008), no. 1, 201-221",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X\\to\\P^n$ be an irreducible holomorphic symplectic manifold of dimension $2n$ fibred over $\\P^n$. Matsushita proved that the generic fibre is a holomorphic Lagrangian abelian variety. In this article we study the discriminant locus $\\Delta\\subset\\P^n$ parametrizing singular fibres. Our main result is a formula for the degree of $\\Delta$, leading to bounds on the degree when $X$ is a four-fold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-07-21T21:37:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C26",
      "14D06"
    ],
    "keywords": [
      "discriminant locus",
      "lagrangian fibration",
      "holomorphic lagrangian abelian variety",
      "irreducible holomorphic symplectic manifold",
      "main result"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7558S"
    }
  }
}