Abstract
Let L be an invertible sheaf on a smooth curve C. A generalized inflection point of L is an inflection point of \(L^{\otimes n}\) for some integer n > 0. A generalized inflection point P of L is called strongly normal if there is a unique integer n > 0 such that P is an inflection point of \(L^{\otimes n}\) and moreover its inflection weight is equal to 1. In case L is a very general invertible sheaf of degree x on C then all generalized inflection points of L are strongly normal.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Arbarello, E., Cornalba, M., Griffiths, P., Harris., J.: Geometry of algebraic curves, Vol I, series, Grundlehren, vol. 267 (1985)
Cukiermann F., Fong L.-Y. (1991). On higher Weierstrass points. Duke Math. J. 62: 179–203
Farkas, G.: Higher order ramification and varieties of secant divisors on the generic curve (2007, preprint)
Fulton W., Lazarsfeld R. (1981). On the connectedness of degeneration loci and special divisors. Acta Math. 146: 271–283
Lax R.F. (1989). Normal higher Weierstrass points. Tsubuka J. Math. 13: 1–5
Silverman J.H., Voloch J.F. (1991). Multiple Weierstrass points. Comp. Math. 79: 123–134
Author information
Authors and Affiliations
Corresponding author
Additional information
The author is affiliated with the University of Leuven as a research fellow Partially supported by the Fund of Scientific Research, Flanders (G.0318.06).
Rights and permissions
About this article
Cite this article
Coppens, M. Generalized inflection points of very general line bundles on smooth curves. Annali di Matematica 187, 605–609 (2008). https://doi.org/10.1007/s10231-007-0058-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10231-007-0058-x