Geometric invariant theory for polarized curves /

Geometric invariant theory for polarized curves /

Saved in:

Bibliographic Details
Author / Creator:	Bini, Gilberto, author.
Imprint:	Cham [Switzerland] : Springer, [2014]
Description:	1 online resource (x, 211 pages) : illustrations.
Language:	English
Series:	Lecture notes in mathematics, 1617-9692 ; 2122 Lecture notes in mathematics (Springer-Verlag) ; 2122.
Subject:	Geometry, Algebraic. Invariants. Moduli theory. Geometry, Algebraic. Invariants. Moduli theory.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11089497

Hidden Bibliographic Details
Other authors / contributors:	Felici, Fabio (Mathematician), author. Melo, Margarida (Mathematician), author. Viviani, Filippo, author.
ISBN:	9783319113371 3319113372 9783319113364 3319113364
Digital file characteristics:	text file PDF
Notes:	Includes bibliographical references and index. Online resource; title from PDF title page (SpringerLink, viewed November 12, 2014).
Summary:	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
Other form:	Printed edition: 9783319113364
Standard no.:	10.1007/978-3-319-11337-1

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.