THE HILBERT SCHEMES OF DEGREE-3 CURVES

Authors
NOLLET S
Citation
S. Nollet, THE HILBERT SCHEMES OF DEGREE-3 CURVES, Annales Scientifiques de l'Ecole Normale Superieure, 30(3), 1997, pp. 367-384
Citations number
15
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Annales Scientifiques de l'Ecole Normale Superieure → ACNP
ISSN journal
00129593
Volume
30
Issue
3
Year of publication
1997
Pages
367 - 384
Database
ISI
SICI code
0012-9593(1997)30:3<367:THSODC>2.0.ZU;2-2
Abstract
In this paper we show that the Hilbert scheme H(3,g) of locally Cohen- Macaulay curves in P-3 of degree three and genus g is connected. This is achieved by giving a classification of these curves, determining th e irreducible components of H(3,g), and giving certain specializations to show connectedness. As a byproduct, we And that there are curves w hich lie in the closure of each irreducible component.