Geometric Invariant Theory for Polarized Curves

Geometric Invariant Theory for Polarized Curves

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 quotie...

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Bibliographic Details
Main Authors: Bini, Gilberto (Author), Felici, Fabio (Author), Melo, Margarida (Author), Viviani, Filippo (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2014.
Series:Lecture Notes in Mathematics, 2122
Subjects:
Mathematics.
Algebraic geometry.
Algebraic Geometry.
Online Access:Full Text via HEAL-Link
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.  .

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