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.
On GIT quotients of Hilbert and Chow schemes of curves / G. Bini, M. Melo, F. Viviani. - In: ELECTRONIC RESEARCH ANNOUNCEMENTS IN MATHEMATICAL SCIENCES. - ISSN 1935-9179. - 19(2012 Jan), pp. 33-40.
On GIT quotients of Hilbert and Chow schemes of curves
G. BiniPrimo
;
2012
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)
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