IJPAM: Volume 78, No. 8 (2012)

CURVES WITH LOW GONALITY AND MAXIMAL RANK

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY


Abstract. For every integer $n\ge 2$ set $\gamma _n:= (n^2-n)/2$. Set $g_2:= 1$, $g_3:= 4$ and $g_n:= \gamma _n+n-2 +g_{n-2}$ for all $n\ge 4$. We prove the following result. Fix integers $n, g,k$ such that $k \ge n\ge 3$. Fix any integer $g $ such that $2k +1 \le g \le g_n$. Let $X$ be a general $k$-gonal curve of genus $g $ and $L$ a general element of $\mbox{\rm Pic}^{g+n}(X)$. Then $L$ is normally generated, i.e. $h_L(X) \subset \mathbb {P}^n$ is projectively normal.

Received: May 26, 2012

AMS Subject Classification: 14H50, 14N05

Key Words and Phrases: gonality, postulation of curves, curves with maximal rank

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 8