Abstract
In this note we compute the number of general points through which a general Brill–Noether space curve passes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arbarello, E., Cornalba, M., Griffiths, P.A., Harris, J.: Geometry of Algebraic Curves. Vol. I, volume 267 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer, New York (1985)
Atanasov, A., Larson, E., Yang, D.: Interpolation for normal bundles of general curves. http://arxiv.org/abs/1509.01724v3
Atanasov, A.V.: Interpolation and vector bundles on curves. ProQuest LLC, Ann Arbor, MI. Thesis (Ph.D.)-Harvard University (2015)
Coskun, I.: Degenerations of surface scrolls and the Gromov-Witten invariants of Grassmannians. J. Algebraic Geom. 15(2), 223–284 (2006)
Debarre, O.: Higher-Dimensional Algebraic Geometry. Universitext. Springer, New York (2001)
Demazure, M., Pinkham, H.C., Teissier, B. (eds.) Séminaire sur les Singularités des Surfaces, volume 777 of Lecture Notes in Mathematics. Springer, Berlin (1980). Held at the Centre de Mathématiques de l’École Polytechnique, Palaiseau, 1976–1977
Ein, L., Lazarsfeld, R.: Stability and restrictions of Picard bundles, with an application to the normal bundles of elliptic curves. In: Complex projective geometry (Trieste, 1989/Bergen, 1989), volume 179 of London Math. Soc. Lecture Note Ser., pp. 149–156. Cambridge Univ. Press, Cambridge (1992)
Griffiths, P., Harris, J.: Principles of Algebraic Geometry. Wiley Classics Library. Wiley, New York (1994). Reprint of the 1978 original
Keem, C., Kim, S.J.: Irreducibility of a subscheme of the Hilbert scheme of complex space curves. J. Algebra 145(1), 240–248 (1992)
Landesman, A.: Interpolation of varieties of minimal degree. http://arxiv.org/abs/1605.01492v1
Landesman, A., Patel, A.: Interpolation problems: Del pezzo surfaces. http://arxiv.org/abs/1601.05840v1
Larson, E.: The generality of a section of a curve. http://arxiv.org/abs/1605.06185v2
Perrin, D.: Courbes passant par \(k\) points généraux de \({\mathbb{P}}^3\). C. R. Acad. Sci. Paris Sér. I Math. 299(10), 451–453 (1984)
Ran, Z.: Normal bundles of rational curves in projective spaces. Asian J. Math. 11(4), 567–608 (2007)
Sacchiero, G.: Normal bundles of rational curves in projective space. Ann. Univ. Ferrara Sez. VII (N.S.), 26, 33–40 (1981), 1980
Stevens, J.: On the number of points determining a canonical curve. Nederl. Akad. Wetensch. Indag. Math. 51(4), 485–494 (1989)
