On a compactification of the moduli space of the rational normal curves
| dc.creator | Cascini, Paolo | |
| dc.date | 1999-12-09 | |
| dc.date | 2000-09-14 | |
| dc.date.accessioned | 2026-07-07T05:32:12Z | |
| dc.date.available | 2026-07-07T05:32:12Z | |
| dc.description | For any odd $n$, we describe a smooth minimal (i.e. obtained by adding an irreducible hypersurface) compactification $\tilde S_n$ of the quasi-projective homogeneous variety $S_{n}=PGL(n+1)/SL(2)$ that parameterizes the rational normal curves in $P^n$. We show that $\tilde S_{n}$ is isomorphic to a component of the Maruyama scheme of the semi-stable sheaves on $P^n$ of rank $n$ and Chern polynomial $(1+t)^{n+2}$ and we compute its Betti numbers. In particular $\tilde S_{3}$ is isomorphic to the variety of nets of quadrics defining twisted cubics, studied by G. Ellinsgrud, R. Piene and S. Strømme (Space curves, Proc. Conf., LNM 1266). | |
| dc.description | 15 pages, ams-latex | |
| dc.identifier | https://arxiv.org/abs/math/9912070 | |
| dc.identifier | http://arxiv.org/abs/math/9912070 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79573 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14F05 | |
| dc.title | On a compactification of the moduli space of the rational normal curves | |
| dc.type | text |