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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Rational nodal curves with no smooth Weierstrass points


Authors: Arnaldo Garcia and R. F. Lax
Journal: Proc. Amer. Math. Soc. 124 (1996), 407-413
MSC (1991): Primary 14H55
MathSciNet review: 1322924
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Abstract: Let $X$ denote the rational curve with $n+1$ nodes obtained from the Riemann sphere by identifying 0 with $\infty $ and $\zeta ^j$ with $-\zeta ^j$ for $j=0,1,\dots ,n-1$, where $\zeta $ is a primitive $(2n)$th root of unity. We show that if $n$ is even, then $X$ has no smooth Weierstrass points, while if $n$ is odd, then $X$ has $2n$ smooth Weierstrass points.


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Additional Information

Arnaldo Garcia
Affiliation: IMPA, Estrada Dona Castorina 110, 22.460 Rio de Janeiro, Brasil
Email: garcia@impa.br

R. F. Lax
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: lax@math.lsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03298-4
PII: S 0002-9939(96)03298-4
Keywords: Weierstrass point, rational nodal curve
Received by editor(s): September 14, 1994
Communicated by: Eric Friedlander
Article copyright: © Copyright 1996 American Mathematical Society