No CrossRef data available.
Article contents
The genus of curves on the three dimensional quadric
Published online by Cambridge University Press: 22 January 2016
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
By means of an ad hoc modification of the so-called “Castelnuovo-Harris analysis” we derive an upper bound for the genus of integral curves on the three dimensional nonsingular quadric which lie on an integral surface of degree 2/c, as a function of k and the degree d of the curve. In order to obtain this we revisit the Uniform Position Principle to make its use computation-free. The curves which achieve this bound can be conveniently characterized.
- Type
- Research Article
- Information
- Copyright
- Copyright © Editorial Board of Nagoya Mathematical Journal 1997
References
[A-C-G-H]
Arbarello, E., Cornalba, M., Griffiths, P. A., Harris, J., Geometry of Algebraic Curves I, Springer, 1985.Google Scholar
[A-S]
Arrondo, E., Sols, I., On Congruences of Lines in the Projective Space, fascicule 3., Mémoire n. 50 Supplément au Bulletin de la S. M. F., 120 (1992), Société Mathématique de France.Google Scholar
[C-C-D]
Chiantini, L., Ciliberto, C., Di Gennaro, V., The genus of projective curves, Duke Math. J., 70 (1993), no. 2, 229–245.Google Scholar
[C-K-M]
Clemens, H., Kollár, J., Mori, S., Higher Dimensional Complex Geometry, Astérisque, 166, Société Mathématique de France (1988).Google Scholar
[D1]
Cataldo, M. A. de, Codimension two subvarieties of quadrics, Ph. D. Thesis Notre Dame (1995).Google Scholar
[D2]
Cataldo, M. A. de, A fimteness theorem for codimension two nonsingular sub-varieties of quadrics, Trans. Amer. Math. Soc, 349 (1997), 2359–2370.Google Scholar
[D3]
Cataldo, M. A. de, Some adjunction-theoretic properties of codimension two nonsingular subvarieties of quadrics, to appear in Can. Jour, of Math..Google Scholar
[D4]
Cataldo, M. A. de, Codimension two nonsingular subvarieties of quadrics: scrolls and classification in degree d ≤ 10, preprint, alg-geom eprints
960–8021.Google Scholar
[E-P]
Ellinsgrud, G., Peskine, C., Sur les surfaces lisses de P4
, Invent. Math., 95 (1989), 1–11.Google Scholar
[G-P]
Gruson, L., Peskine, C., Genre des courbes de l’espace projectif in Proceedings of Tromso (Conference on Algebraic Geometry), LNM 687, Springer (1977), pp. 31–59.Google Scholar
[Mi]
Migliore, J., Liaison of a union of Skew Lines in P4
, Pac. Jour. Math., 130 (1987), no. 1, 153–170.Google Scholar
[Mu]
Mumford, D., Lectures on Curves on an Algebraic Surface, Annals of Mathematics Studies, 59 (1966), Princeton Univ. Press.Google Scholar