Osaka Journal of Mathematics

Algebraic curves violating the slope inequalities

Takao Kato and Gerriet Martens

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The gonality sequence $(d_{r})_{r \ge 1}$ of a curve of genus $g$ encodes, for $r<g$, important information about the divisor theory of the curve. Mostly it is very difficult to compute this sequence. In general it grows rather modestly (made precise below) but for curves with special moduli some ``unexpected jumps'' may occur in it. We first determine all integers $g>0$ such that there is no such jump, for all curves of genus $g$. Secondly, we compute the leading numbers (up to $r=19$) in the gonality sequence of an extremal space curve, i.e. of a space curve of maximal geometric genus w.r.t. its degree.

Article information

Osaka J. Math., Volume 52, Number 2 (2015), 423-439.

First available in Project Euclid: 24 March 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H45: Special curves and curves of low genus
Secondary: 14H51: Special divisors (gonality, Brill-Noether theory)


Kato, Takao; Martens, Gerriet. Algebraic curves violating the slope inequalities. Osaka J. Math. 52 (2015), no. 2, 423--439.

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