The aim of this note is to announce some results on the GIT problem for the Hilbert and Chow scheme of curves of degree d and genus g in P^d-g, whose full details will appear in a subsequent paper. In particular, we extend the previous results of L. Caporaso up to d>4(2g-2) and we observe that this is sharp. In the range 2(2g-2)<7/2(2g-2), we get a complete new description of the GIT quotient. As a corollary, we get a new compactification of the universal Jacobian over the moduli space of pseudo-stable curves.

G. Bini, M. Melo, F. Viviani (2012). On GIT quotients of Hilbert and Chow schemes of curves, 19, 33-40 [10.3934/era.2012.19.33].

On GIT quotients of Hilbert and Chow schemes of curves

G. Bini;
2012-01-01

Abstract

The aim of this note is to announce some results on the GIT problem for the Hilbert and Chow scheme of curves of degree d and genus g in P^d-g, whose full details will appear in a subsequent paper. In particular, we extend the previous results of L. Caporaso up to d>4(2g-2) and we observe that this is sharp. In the range 2(2g-2)<7/2(2g-2), we get a complete new description of the GIT quotient. As a corollary, we get a new compactification of the universal Jacobian over the moduli space of pseudo-stable curves.
Settore MAT/03 - Geometria
http://arxiv.org/abs/1109.3645v2
G. Bini, M. Melo, F. Viviani (2012). On GIT quotients of Hilbert and Chow schemes of curves, 19, 33-40 [10.3934/era.2012.19.33].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/398173
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