Hostname: page-component-745bb68f8f-kw2vx Total loading time: 0 Render date: 2025-01-12T11:38:10.087Z Has data issue: false hasContentIssue false
  • English
  • Français

Weierstrass points on rational nodal curves

Published online by Cambridge University Press:  18 May 2009

R. F. Lax
R. F. Lax
Affiliation:
Louisiana State University, Baton Rouge, LA 70803, U.S.A.
Rights & Permissions [Opens in a new window]

Extract

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.

C. Widland [14] has defined Weierstrass points on integral, projective Gorenstein curves. We show here that the Weierstrass points on a generic integral rational nodal curve have the minimal possible weights or, equivalently, that such a curve has the maximum possible number of distinct nonsingular Weierstrass points. Rational curves with g nodes arise in degeneration arguments involving smooth curves of genus g and they have also recently arisen in connection with g-soliton solutions to certain nonlinear partial differential equations [11], [13].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 29 , Issue 1 , January 1987 , pp. 131 - 140
Copyright
Copyright © Glasgow Mathematical Journal Trust 1987

References

REFERENCES

1.Diaz, S., Exceptional Weierstrass points and the divisor on moduli space that they define, Memoirs Amer. Math. Vol. 56, No. 327, 1985.Google Scholar
2.Fulton, W., Intersection theory (Springer-Verlag, 1984).CrossRefGoogle Scholar
3.Hartshorne, R., Residues and duality, Lecture Notes in Mathematics No. 20 (Springer-Verlag, 1966).CrossRefGoogle Scholar
4.Hartshorne, R., Algebraic geometry (Springer-Verlag, 1977).CrossRefGoogle Scholar
5.Kempf, G. and Laksov, D., The determinantal formula of Schubert calculus, Ada Math. 132 (1974), 153–162.Google Scholar
6.Kleiman, S., r-special subschemes and an argument of Seven's, Advances in Math. 22 (1976), 1–23.CrossRefGoogle Scholar
7.Lax, R. F., On the dimension of varieties of special divisors, Trans. Amer. Math. Soc. 203 (1975), 141–159.CrossRefGoogle Scholar
8.Lax, R. F., Weierstrass points of the universal curve, Math. Ann. 216 (1975), 35–42.CrossRefGoogle Scholar
9.Lax, R. F., Gap sequences and moduli in genus 4, Math. Z. 175 (1980), 67–75.CrossRefGoogle Scholar
10.Lax, R. F. and Widland, C., Weierstrass points on rational nodal curves of genus 3, preprint.Google Scholar
11.Mumford, D., Tata Lectures on Theta II (Birkhäuser, Boston, 1984).Google Scholar
12.Piene, R., Numerical characters of a curve in projective n-space. pp. 475–495, Real and complex singularities, Oslo, 1976 (Sijthoff and Nordhoff, Netherlands, 1977).CrossRefGoogle Scholar
13.Previato, E., Hyperelliptic quasi-periodic and soliton solutions of the nonlinear Schrodinger equation, Duke Math. J. 52 (1985), 329–377.CrossRefGoogle Scholar
14.Widland, C., On Weierstrass points of Gorenstein curves, Ph. D. dissertation, Louisiana State University 1984.Google Scholar