Geometric Invariant Theory for Polarized Curves: 2122 - Brossura

Bini, Gilberto; Felici, Fabio; Melo, Margarida; Viviani, Filippo

Brossura

ISBN 10: 3319113364 ISBN 13: 9783319113364

Casa editrice: Springer, 2014

Riassunto

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

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Contenuti

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.

 

Dettagli dell?edizione

• Editore: Springer
• Data di pubblicazione: 2014
• ISBN 10: 3319113364
• ISBN 13: 9783319113364
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 224