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...

Ausführliche Beschreibung

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Bibliographische Detailangaben
Hauptverfasser: Bini, Gilberto, Felici, Fabio, Melo, Margarida, Viviani, Filippo
Format: Buch
Sprache:eng
Schlagworte:
Algebraic Geometry
Geometry
Geometry, Algebraic
Invariants
Mathematics
Mathematics and Statistics
Moduli theory
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Beschreibung
Zusammenfassung: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
ISSN:0075-8434
1617-9692
DOI:10.1007/978-3-319-11337-1