On GIT quotients of Hilbert and Chow schemes of curves

Gilberto Bini; Margarida Melo; Filippo Viviani

doi:10.3934/era.2012.19.33

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arXiv · 1109.3645

On GIT quotients of Hilbert and Chow schemes of curves

Gilberto Bini·Margarida Melo·Filippo Viviani

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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.

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BibTeX RIS

Gilberto Bini, Margarida Melo, Filippo Viviani. 2011-09-16. On GIT quotients of Hilbert and Chow schemes of curves. https://doi.org/10.3934/era.2012.19.33

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