The Hilbert Schemes of Degree Three Curves are Connected
| dc.creator | Nollet, Scott | |
| dc.date | 1996-03-14 | |
| dc.date.accessioned | 2026-07-07T09:06:44Z | |
| dc.date.available | 2026-07-07T09:06:44Z | |
| dc.description | In this paper we show that the Hilbert scheme $H(3,g)$ of locally Cohen-Macaulay curves in $\Pthree$ of degree three and genus $g$ is connected. In contrast to $H(2,g)$, which is irreducible, $H(3,g)$ generally has many irreducible components (roughly $-g/3$ of them). To show connectedness, we classify the curves (giving particular attention to the triple lines), determine the irreducible components, and give flat families over $\Aone$ to show that the components meet. As a byproduct, we find that there are curves which lie in the closure of each irreducible component. | |
| dc.description | 20 pages, Latex | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9603011 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9603011 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150122 | |
| dc.subject | Algebraic Geometry | |
| dc.title | The Hilbert Schemes of Degree Three Curves are Connected | |
| dc.type | text |