{
  "id": "math/0402197",
  "version": "v2",
  "published": "2004-02-12T12:15:08.000Z",
  "updated": "2006-07-09T16:15:02.000Z",
  "title": "Multiple Saddle Connections on Flat Surfaces and Principal Boundary of the Moduli Spaces of Quadratic Differentials",
  "authors": [
    "Howard Masur",
    "Anton Zorich"
  ],
  "comment": "We have completely rewritten the first version of the paper. Though the initial version did not contain mistakes in mathematics, the style of presentation was somehow too descriptive. We formalized our constructions elaborating appropriate language of combinatorial geometry (ribbon graphs, configurations, ...) which made the paper much shorter, despite the fact that now it is completed with numerous examples",
  "journal": "Geom. Funct. Anal. 18 (2008), no. 3, 919-987",
  "categories": [
    "math.GT",
    "math.AG"
  ],
  "abstract": "We describe typical degenerations of quadratic differentials thus describing ``generic cusps'' of the moduli space of meromorphic quadratic differentials with at most simple poles. The part of the boundary of the moduli space which does not arise from ``generic'' degenerations is often negligible in problems involving information on compactification of the moduli space. However, even for a typical degeneration one may have several short loops on the Riemann surface which shrink simultaneously. We explain this phenomenon, describe all rigid configurations of short loops, present a detailed description of analogs of desingularized stable curves arising here, and show how one can reconstruct a Riemann surface endowed with a quadratic differential which is close to a ``cusp'' by the corresponding point at the principal boundary.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-07-09T16:15:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moduli space",
      "multiple saddle connections",
      "principal boundary",
      "flat surfaces",
      "riemann surface"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......2197M"
    }
  }
}