rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Geometric Invariant Theory for Polarized Curves
  name:
    name part: Bini, Gilberto.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Felici, Fabio.
    role:
      role term: author.
  name:
    name part: Melo, Margarida.
    role:
      role term: author.
  name:
    name part: Viviani, Filippo.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2014
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: X, 211 p. 17 illus. online resource.
  abstract: We investigate GIT quotients of polarized curves. More specifically, we study the GIT problem for the Hilbert and Chow schemes of curves of degree d and genus g in a projective space of dimension d-g, as d decreases with respect to g. We prove that the first three values of d at which the GIT quotients change are given by d=a(2g-2) where a=2, 3.5, 4. We show that, for a>4, L. Caporaso's results hold true for both Hilbert and Chow semistability. If 3.5<a<4, the Hilbert semistable locus coincides with the Chow semistable locus and it maps to the moduli stack of weakly-pseudo-stable curves. If 2<a<3.5, the Hilbert and Chow semistable loci coincide and they map to the moduli stack of pseudo-stable curves. We also analyze in detail the critical values a=3.5 and a=4, where the Hilbert semistable locus is strictly smaller than the Chow semistable locus. As an application, we obtain three compactications of the universal Jacobian over the moduli space of stable curves, weakly-pseudo-stable curves and pseudo-stable curves, respectively.
  table of contents: Introduction -- Singular Curves -- Combinatorial Results -- Preliminaries on GIT -- Potential Pseudo-stability Theorem -- Stabilizer Subgroups -- Behavior at the Extremes of the Basic Inequality -- A Criterion of Stability for Tails -- Elliptic Tails and Tacnodes with a Line -- A Strati_cation of the Semistable Locus -- Semistable, Polystable and Stable Points (part I) -- Stability of Elliptic Tails -- Semistable, Polystable and Stable Points (part II) -- Geometric Properties of the GIT Quotient -- Extra Components of the GIT Quotient -- Compacti_cations of the Universal Jacobian -- Appendix: Positivity Properties of Balanced Line Bundles. .
  note: by Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani.
  subject:
    topic: Mathematics
  subject:
    topic: Algebraic geometry
  subject:
    topic: Mathematics
  subject:
    topic: Algebraic Geometry
  classification: QA564-609
  classification: 516.35
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes in Mathematics, 2122
  identifier: 9783319113371
  identifier: http://dx.doi.org/10.1007/978-3-319-11337-1
  record info:
    record creation date: 141107
    record change date: 20151103123855.0
    record identifier: 978-3-319-11337-1