Geometric invariant theory for polarized curves / Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani.

Author
Bini, Gilberto [Browse]
Format
Book
Language
English
Published/​Created
  • Cham : Springer, [2014]
  • ©2014
Description
x, 211 pages : illustrations ; 24 cm

Availability

Copies in the Library

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Lewis Library - Stacks QA3 .L28 no.2122 Browse related items Request

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    Subject(s)
    Author
    Series
    • Lecture notes in mathematics (Springer-Verlag) ; 2122. [More in this series]
    • Lecture notes in mathematics, 0075-8434 ; 2122
    Summary note
    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
    Bibliographic references
    Includes bibliographical references (pages 205-208) and index.
    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 stratification 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
    • Compactification of the universal Jacobian
    • Appendix: positivity properties of balanced line bundles.
    Other format(s)
    Also available in an electronic version.
    ISBN
    • 9783319113364 ((paperback))
    • 3319113364 ((paperback))
    LCCN
    2014954809
    OCLC
    888551930
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