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# smoothCanonicalCurveGenus14 -- Compute a random canonical curve of genus 14

- Usage:
    `smoothCanonicalCurveGenus14(p)`
- Inputs:
  - p, an integer, a prime number defining the characteristic
- Optional inputs:
  - Details => ..., default value false, keeps track of the precise step in the construction of canonical genus 14 and 15 curves. Default value is "false".
  - Printing => ..., default value false, displays information about the current step in the constructions. Default value is "false".
- Outputs:
  - ICan, an ideal, the ideal of a smooth canonically embedded genus 14 curve

## Description

Computes a smooth canonical curve of genus 14 over a field of characteristc p. The constructions are based on the unirationality proof of M_14 by A. Verra (See "http://arxiv.org/abs/math/0402032") and the methods in the Macaulay2-Package "RandomGenus14Curves". A unirational parametrization of M_g is only a rational map and bad choices of parameters (which are quite likely over small fields) might end up in the indeterminacy locus or some other undesired subloci. In this constructions we catch the steps which do not work out for very small characteristic.

If the option Printing is set to true then printings about the current step in the construction are displayed.

## See also

- smoothCanonicalCurve -- Computes the ideal of canonical curve
- smoothCanonicalCurveViaPlaneModel -- Computes the ideal of canonical curve via plane models
- smoothCanonicalCurveViaSpaceModel -- Computes the ideal of canonical curve via space models
- smoothCanonicalCurveGenus15 -- Computes the ideal of canonical curve of genus 15

## Ways to use smoothCanonicalCurveGenus14:

- `smoothCanonicalCurveGenus14(ZZ)`

## For the programmer

The object smoothCanonicalCurveGenus14 is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/RandomCurvesOverVerySmallFiniteFields.m2:1259:0.