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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.
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Abstract

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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

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