Bibliographic Information

Geometric invariant theory for polarized curves

Gilberto Bini ... [et al.]

(Lecture notes in mathematics, 2122)

Springer, c2014

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Note

Other authors: Fabio Felici, Margarida Melo, Filippo Viviani

Includes bibliographical references (p. 205-208) and index

Description and Table of Contents

Description

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

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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Details

  • NCID
    BB17360431
  • ISBN
    • 9783319113364
  • LCCN
    2014954809
  • Country Code
    sz
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Cham
  • Pages/Volumes
    x, 211 p.
  • Size
    24 cm
  • Parent Bibliography ID
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