# Forgetful linear systems on the projective space and rational normal curves over ℳ0,2nGIT

@article{Bolognesi2011ForgetfulLS,
title={Forgetful linear systems on the projective space and rational normal curves over ℳ0,2nGIT},
author={M. Bolognesi},
journal={Bulletin of The London Mathematical Society},
year={2011},
volume={43},
pages={583-596}
}
• M. Bolognesi
• Published 2011
• Mathematics
• Bulletin of The London Mathematical Society
Let $\cM_{0,n}$ the moduli space of $n$-pointed rational curves. The aim of this note is to give a new, geometric construction of $\cM_{0,2n}^{GIT}$, the GIT compacification of $\cM_{0,2n}$, in terms of linear systems on $\PP^{2n-2}$ that contract all the rational normal curves passing by the points of a projective base. These linear systems are a projective analogue of the forgetful maps between $\bar{\cM}_{0,2n+1}$ and $\bar{\cM}_{0,2n}$. The construction is performed via a study of the so… Expand
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