On GIT quotients of Hilbert and Chow schemes of curves
Algebraic Geometry
2012-02-14 v2
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)<d<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.
Cite
@article{arxiv.1109.3645,
title = {On GIT quotients of Hilbert and Chow schemes of curves},
author = {Gilberto Bini and Margarida Melo and Filippo Viviani},
journal= {arXiv preprint arXiv:1109.3645},
year = {2012}
}
Comments
8 pages, final version, to appear in Electron. Res. Announc. Math. Sci