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KoszulDivisorOnPic14M8 :: randomCurveGenus8Degree14inP6

randomCurveGenus8Degree14inP6 -- compute a random normal curve of genus g=8 and degree 14 in P^6

Synopsis

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 P⁶

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 : FF=ZZ/10007;S=FF[x_0..x_6];

i3 : I=randomCurveGenus8Degree14inP6 S;

o3 : Ideal of S

i4 : betti res I

            0 1  2  3  4 5
o4 = total: 1 7 35 56 35 8
         0: 1 .  .  .  . .
         1: . 7  .  .  . .
         2: . . 35 56 35 8

o4 : BettiTally

Ways to use `randomCurveGenus8Degree14inP6` :

randomCurveGenus8Degree14inP6(PolynomialRing)