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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
Available Online
Online Content
Springer Nature - Springer Mathematics and Statistics eBooks 2014 English International
Springer Nature - Springer Lecture Notes in Mathematics eBooks
Copies in the Library
Location
Call Number
Status
Location Service
Notes
Lewis Library - Stacks
QA3 .L28 no.2122
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Details
Subject(s)
Geometry, Algebraic
[Browse]
Invariants
[Browse]
Moduli theory
[Browse]
Author
Felici, Fabio (Mathematician)
[Browse]
Melo, Margarida (Mathematician)
[Browse]
Viviani, Filippo
[Browse]
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.
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Other format(s)
Also available in an electronic version.
ISBN
9783319113364 ((paperback))
3319113364 ((paperback))
LCCN
2014954809
OCLC
888551930
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Other versions
Geometric Invariant Theory for Polarized Curves [electronic resource] / by Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani.
id
99125130005906421