Geometric Invariant Theory for Polarized Curves
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ISBN-13:
9783319113364
Veröffentl:
2014
Einband:
Paperback
Erscheinungsdatum:
19.11.2014
Seiten:
224
Autor:
Gilberto Bini
Gewicht:
347 g
Format:
235x155x13 mm
Serie:
2122, Lecture Notes in Mathematics
Sprache:
Englisch
Beschreibung:
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
An introduction to the techniques of Geometric Invariant Theory via a detailed analysis of the GIT problem for polarized curves
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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