Geometric Invariant Theory for Polarized Curves

Gilberto Bini (u. a.)

ISBN 10: 3319113364 / ISBN 13: 9783319113364

Published by Springer, 2014

About this Item

Geometric Invariant Theory for Polarized Curves | Gilberto Bini (u. a.) | Taschenbuch | Lecture Notes in Mathematics | x | Englisch | 2014 | Springer | EAN 9783319113364 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.

Seller Inventory # 105170353

Bibliographic Details

• Title: Geometric Invariant Theory for Polarized Curves
• Publisher: Springer
• Publication Date: 2014
• Language: English
• ISBN 10: 3319113364
• ISBN 13: 9783319113364
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 13D millimeters 235 millimeters width by 155 millimeters height by 13 millimeters depth
• Weight: 347 grams
• Seller catalogs:
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About this title

Synopsis

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.