IJPAM: Volume 2, No. 4 (2002)

WEIERSTRASS POINTS AND WEIERSTRASS
PAIRS ON ALGEBRAIC CURVES

E. Ballico
Dept. of Mathematics
University of Trento
38050 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Here we prove (in characteristic $0$) the following result. Fix integers $k$, $g$ such that $g\ge 13$ and $k\ge 4$. Then a general $k$-gonal curve of genus $g$ has only ordinary Weierstrass points, only finitely many Weierstrass pairs of weight at least two and no Weierstrass pair of weight at least $3$.

Received: May 4, 2002

AMS Subject Classification: 14H55

Key Words and Phrases: Weierstrass point, Weierstrass pair, $k$-gonal curve, curves with general moduli

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2002
Volume: 2
Issue: 4