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# randomCurveGenus8Degree14inP6 -- Compute a random normal curve of genus g=8 and degree 14 in \PP^6

- Usage:
    `I=randomCurveGenus8Degree14inP6 S`
- Inputs:
  - S, a polynomial ring, in 7 variables
- Outputs:
  - I, an ideal, of a curve of geometric genus 8 and degree 14 in \PP^6

## Description

The construction is based on Mukai's unirational description of $M_{8,8}$ of the moduli space of genus 8 with 8 marked points (see [Mu]).

    i1 : setRandomSeed("alpha");
     -- setting random seed to 10206284518

    i2 : FF=ZZ/10007;

    i3 : S=FF[x_0..x_6];

    i4 : I=randomCurveGenus8Degree14inP6 S;

    o4 : Ideal of S

    i5 : betti res I

                0 1  2  3  4 5
    o5 = total: 1 7 35 56 35 8
             0: 1 .  .  .  . .
             1: . 7  .  .  . .
             2: . . 35 56 35 8

    o5 : BettiTally

## Ways to use randomCurveGenus8Degree14inP6:

- `randomCurveGenus8Degree14inP6(PolynomialRing)`

## For the programmer

The object randomCurveGenus8Degree14inP6 is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/RandomGenus14Curves.m2:283:0.