IJPAM: Volume 19, No. 1 (2005)

WEIERSTRASS SETS AND RAMIFICATION
POINTS OF LINE BUNDLES ON CURVES

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 curve of genus $g$, $L\in \mbox{\rm Pic}(X)$ and $(P_1,\dots ,P_n)\in X$ with $P_i \ne P_j$ for all $i\ne j$. $(P_1,\dots ,P_n)$ is a Weierstrass (resp. strict Weierstrass) $n$-ple for $L$ if there are integers $a_i\ge 0$ (resp. $a_i>0$) such that $\sum _{i=1}^{n} a_i \le h^0(X,L)$ and $h^0(X,L(-a_1P_1- \cdots -P_n)) > h^0(X,L) - \sum _{i=1}^{n} a_i$. Here we study $n$-ples which are Weierstrass $n$-ples for large classes of line bundles on $X$, mainly when $n \le 2$.

Received: January 31, 2005

AMS Subject Classification: 14H55

Key Words and Phrases: Weierstrass point, Weierstrass $n$-ple, Weierstrass pair, gap sequence, ramification point

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 19
Issue: 1