Osculating degeneration of curves
| dc.contributor.author | Mallavibarrena Martínez de Castro, Raquel | |
| dc.contributor.author | González Pascual, Sonia | |
| dc.date.accessioned | 2023-06-20T16:59:18Z | |
| dc.date.available | 2023-06-20T16:59:18Z | |
| dc.date.issued | 2003 | |
| dc.description.abstract | The main objects of this paper are osculating spaces of order m to smooth algebraic curves, with the property of meeting the curve again. We prove that the only irreducible curves with an infinite number of this type of osculating spaces of order m are curves in Pm+1 Whose degree n is greater than m + 1. This is a generalization of the result and proof of Kaji (Kaji, H. (1986). On the tangentially degenerate curves. J. London Math. Soc. 33(2)-430-440) that corresponds to the case m = 1. We also obtain an enumerative formula for the number of those osculating spaces to curves in Pm+2. The case m = 1 of it is a classical formula proved with modern techniques. by Le Barz (Le Barz, P. (1982). Formules multisecantes pour les courbes gauches quelconques. In: Enumerative Geometry and Classical Algebraic Geometry. Prog. in Mathematics 24, Birkhauser, pp. 165-197). | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/16624 | |
| dc.identifier.doi | 10.1081/AGB-120022445 | |
| dc.identifier.issn | 0092-7872 | |
| dc.identifier.officialurl | http://www.tandfonline.com/doi/pdf/10.1081/AGB-120022445 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57577 | |
| dc.issue.number | 8 | |
| dc.journal.title | Communications in Algebra | |
| dc.language.iso | eng | |
| dc.page.final | 3845 | |
| dc.page.initial | 3829 | |
| dc.publisher | Taylor & Francis | |
| dc.relation.projectID | BFM2000-0621 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 512.774 | |
| dc.subject.keyword | osculating space | |
| dc.subject.keyword | Hilbert scheme of points | |
| dc.subject.keyword | curve | |
| dc.subject.keyword | enumerative formula | |
| dc.subject.ucm | Geometria algebraica | |
| dc.subject.unesco | 1201.01 Geometría Algebraica | |
| dc.title | Osculating degeneration of curves | |
| dc.type | journal article | |
| dc.volume.number | 31 | |
| dcterms.references | Arbarello, E., Cornalba, M., Griffiths, Ph., Harris, J. (1977). Geometry of Algebraic Curves. Vol. I. New York, Springer-Verlag. Hartshorne, R. (1977). Algebraic Geometry. Graduate Texts in Mathematics, Berlin: Springer. Iarrobino, A. (1987). Hilbert scheme of points: Overview of last ten years. In: Algebraic Geometry, Proc. Symp. Pure Maths. No. 46, part 2, AMS, pp. 297–320. Kaji, H. (1986). On the tangentially degenerate curves. J. London Math. Soc. 33(2):430–440. Kleiman, S. L.(1976).The enumerative theory of singularities.In: Real and Complex Singularities. Oslo. Sijthoff and Noordhoff, pp. 287–396. Le Barz, P. (1982). Formules multisécantes pour les courbes gauches quelconques. In: Enumerative Geometry and Classical Algebraic Geometry. Prog. in Mathematics 24, Birkhäuser, pp. 165–197. Le Barz, P. (1987). Quelques calculs dans les variétés d'alignements. Adv. in Math. 64(2):87–117. Mallavibarrena, R. (1986). Validité de la formule classique des trisécantes stationnaires. C. R. Acad. Sci. Paris Sér. I Math. 303:799–802. Piene, R. (1976). Numerical characters of a curve in projective N-Space. In: Real and Complex Singularities. Oslo: Sijthoff and Noordhoff, pp. 475–495 Pohl, W. F. (1962). Differential geometry of higher order. Topology 1:169–211. Vassallo, V. (1994). Justification de la méthode fonctionelle pour les courbes gauches. Acta Math. 172:257–297. | |
| dspace.entity.type | Publication |
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