# smoothCanonicalCurveViaSpaceModel -- Computes the ideal of canonical curve via space models

## Synopsis

• Usage:
smoothCanonicalCurveViaSpaceModel(g,p)
• Inputs:
• g, an integer, the genus
• p, an integer, a prime number defining the characteristic
• Optional inputs:
• 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) canonical curve of genus g over a field with characteristic p

## Description

Computes a smooth canonical curve of genus g over a field of characteristc p. The constructions are based on the unirationality proofs of M_g for g<=10 and the methods in the RandomCurves-package. 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. The Function works for 11<=g<=13.

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