GEOMETRIC INVARIANT THEORY FOR POLARIZED CURVES

GEOMETRIC INVARIANT THEORY FOR POLARIZED CURVES

Editorial:
SPRINGER
Año de edición:
Materia
Matematicas
ISBN:
978-3-319-11336-4
Páginas:
211
N. de edición:
1
Idioma:
Inglés
Ilustraciones:
17
Disponibilidad:
Disponible en 2-3 semanas

Descuento:

-5%

Antes:

37,10 €

Despues:

35,25 €

•An introduction to the techniques of Geometric Invariant Theory via a detailed analysis of the GIT problem for polarized curves
•An introduction to the problem of compactifying moduli spaces through an interpretation of the output of the GIT analysis
•An introduction to the rich theory of compactified Jacobians for singular curves via three explicit examples
•A detailed description of the quotient stacks associated to the different GIT quotients, illustrating the interplay between these two techniques

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
Table of contents (17 chapters)
1.Introduction
2.Singular Curves
3.Combinatorial Results
4.Preliminaries on GIT
5.Potential Pseudo-Stability Theorem
6.Stabilizer Subgroups
7.Behavior at the Extremes of the Basic Inequality
8.A Criterion of Stability for Tails
9.Elliptic Tails and Tacnodes with a Line
10.A Stratification of the Semistable Locus
11.Semistable, Polystable and Stable Points (Part I)
12.Stability of Elliptic Tails
13.Semistable, Polystable and Stable Points (Part II)
14.Geometric Properties of the GIT Quotient
15.Extra Components of the GIT Quotient
16.Compactifications of the Universal Jacobian
17.Appendix: Positivity Properties of Balanced Line Bundles