Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T05:49:27.602Z Has data issue: false hasContentIssue false
  • English
  • Français

Distribution of Weierstrass Points on Rational Cuspidal Curves

Published online by Cambridge University Press:  20 November 2018

John B. Little
John B. Little*
Affiliation:
Department of Mathematics, College of the Holy Cross, Worcester, MA 01610, U.S.A.
Rights & Permissions [Opens in a new window]

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.

We study the set W(𝓛) of Weierstrass points of all positive tensor powers of an invertible sheaf 𝓛 on an irreducible rational curve X with g ≧ 2 ordinary cusps. Using an idea from B. Olsen's study of the analogous question on smooth curves, and an explicit formula for the "theta function" of a cuspidal rational curve, we show that W(𝓛) is never dense on X (in contrast to the case of smooth curves of genus g ≧ 2).

Keywords

14F0714H2014H40
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 2 , 01 June 1990 , pp. 184 - 189
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Ancona, V., On the Abel-Jacobi Theorem for Singular Curves (Italian), Seminari di Geometria 1984, Univ. Stud. Bologna, Bologna, 1985, 3–6.Google Scholar
2. Lax, R. F., Weierstrass Points on Rational Nodal Curves, Glasgow Math. J., 29 (1987), 131–140.Google Scholar
3. Lax, R. F., On the Distribution of Weierstrass Points on Singular Curves, Israel J. Math. 57 (1987), 107–115.Google Scholar
4. Lax, R. F., and Widland, C., Weierstrass Points on Rational Cuspidal Curves, to appear Bolletino U.M. Italiano.Google Scholar
5. Little, J., and Furio, K., On the Distribution of Weierstrass Points on Irreducible Rational Nodal Curves, preprint.Google Scholar
6. Olsen, B., On Higher Order Weierstrass Points, Ann. of Math. 95 (1972), 351–364.Google Scholar