dc.contributor.author | Kleppe, Jan Oddvar | |
dc.date.accessioned | 2011-12-08T09:15:43Z | |
dc.date.available | 2011-12-08T09:15:43Z | |
dc.date.issued | 2012 | |
dc.identifier.citation | Kleppe, J.O. (2012). The Hilbert Scheme of Buchsbaum space curves. Annales de l'Institut Fourier, 62 | en_US |
dc.identifier.issn | 0373-0956 | |
dc.identifier.uri | https://hdl.handle.net/10642/998 | |
dc.description.abstract | We consider the Hilbert scheme H(d,g) of space curves C with homogeneous ideal I(C):=H_{*}^0(\sI_C) and Rao module M:=H_{*}^1(\sI_C). By taking suitable generizations (deformations to a more general curve C') of C, we simplify the minimal free resolution of I(C) by e.g. making consecutive free summands (ghost-terms) disappear in a free resolution of I(C'). Using this for Buchsbaum curves of diameter one (M_v \ne 0 for only one v), we establish a one-to-one correspondence between the set \sS of irreducible components of H(d,g) that contain (C) and a set of minimal 5-tuples that specializes in an explicit manner to a 5-tuple of certain graded Betti numbers of C related to ghost-terms. Moreover we almost completely (resp. completely) determine the graded Betti numbers of all generizations of C (resp. all generic curves of \sS), and we give a specific description of the singular locus of the Hilbert scheme of curves of diameter at most one. We also prove some semi-continuity results for the graded Betti numbers of any space curve under some assumptions. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Association des Annales de l'Institute Fourier | en_US |
dc.relation.ispartofseries | Annales de l'Institut Fourier;62 | |
dc.subject | Hilbert scheme | en_US |
dc.subject | Space curve | en_US |
dc.subject | Buchsbaum curve | en_US |
dc.subject | Graded Betti numbers | en_US |
dc.subject | Ghost term | en_US |
dc.subject | Linkage | en_US |
dc.subject | VDP::Matematikk og Naturvitenskap: 400::Matematikk: 410 | en_US |
dc.title | The Hilbert Scheme of Buchsbaum space curves | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.description.version | Postprint | en_US |