Geometric Invariant Theory for Polarized Curves by Gilberto BiniGeometric Invariant Theory for Polarized Curves by Gilberto Bini

Geometric Invariant Theory for Polarized Curves

byGilberto Bini, Fabio Felici, Margarida Melo

Paperback | November 19, 2014

Pricing and Purchase Info

$62.06 online 
$68.95 list price save 9%
Earn 310 plum® points

Prices and offers may vary in store


In stock online

Ships free on orders over $25

Not available in stores


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&a&4, the Hilbert semistable locus coincides with the Chow semistable locus and it maps to the moduli stack of weakly-pseudo-stable curves. If 2&a&3.5, the Hilbert and Chow semistable loci coincide and they map to the moduli stack of pseudo-stable curves. We also analyze in detail the critical values a=3.5 and a=4, where the Hilbert semistable locus is strictly smaller than the Chow semistable locus. As an application, we obtain three compactications of the universal Jacobian over the moduli space of stable curves, weakly-pseudo-stable curves and pseudo-stable curves, respectively.

Title:Geometric Invariant Theory for Polarized CurvesFormat:PaperbackDimensions:211 pagesPublished:November 19, 2014Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319113364

ISBN - 13:9783319113364


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.