## Osaka Journal of Mathematics

### Algebraic curves violating the slope inequalities

#### Abstract

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

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

Dates
First available in Project Euclid: 24 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1427202895

Mathematical Reviews number (MathSciNet)
MR3326619

Zentralblatt MATH identifier
1330.14054

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

#### Citation

Kato, Takao; Martens, Gerriet. Algebraic curves violating the slope inequalities. Osaka J. Math. 52 (2015), no. 2, 423--439. https://projecteuclid.org/euclid.ojm/1427202895

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