IJPAM: Volume 22, No. 1 (2005)

ON THE EXISTENCE OF CURVES WITH ONE OR
MORE WEIERSTRASS POINTS WITH
A CERTAIN SEMIGROUP

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Let $X$ be a smooth projective curve of genus $g \ge 4$ and $Q\in X$. Here we will find (if $g \gg z \ge 1$ and $g \gg k \ge 4$) a smooth genus $g$ curve $X$ and $Q_1,\dots ,Q_z \in X$, $Q_i \ne Q_j$ for all $i\ne j$, with the same Weierstrass semigroup whose first non-gap is $k$ and the other generators ``prescribed'' (freely depending on one integer parameter).

Received: May 24, 2005

AMS Subject Classification: 14H55

Key Words and Phrases: Weierstrass point, Weierstrass semigroup, $k$-gonal curve, Hirzebruch surface

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 22
Issue: 1