## Rational nodal curves with no smooth Weierstrass points

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- by Arnaldo Garcia and R. F. Lax PDF
- Proc. Amer. Math. Soc.
**124**(1996), 407-413 Request permission

## 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.## References

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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
- Received by editor(s): September 14, 1994
- Communicated by: Eric Friedlander
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**124**(1996), 407-413 - MSC (1991): Primary 14H55
- DOI: https://doi.org/10.1090/S0002-9939-96-03298-4
- MathSciNet review: 1322924