IJPAM: Volume 81, No. 6 (2012)

ON THE GONALITY SEQUENCE AND THE BIRATIONAL
GONALITY SEQUENCE OF SMOOTH CURVES

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: [email protected]


Abstract. Let $C$ be a smooth curve of genus $g$. For any integer $r\ge 2$ the $r$-gonality of $C$ is a minimal degree of a line bundle $L$ such that $h^0(C,L)=r+1$. If we assume that the associated map $C\to \mathbb {P}^r$ is birational onto its image, then we get the $r$-birational gonality $s_r(C)$. For $g=29,30$ we prove the existence of $C$ with $d_2(C)=10$ and $d_3(C)=16$. For many genera we prove the existence of $C$ with $s_4(C)/4 > s_3(C)/3$ and $s_6(C)/6 > s_5(C)$ (both inequalities for the same curve).

Received: October 8, 2012

AMS Subject Classification: 14H45, 14H50, 32L10

Key Words and Phrases: gonality sequence, birational gonality sequence, slope inequality, smooth curve, nodal curve

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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: 81
Issue: 6