i2 : time X = specialGushelMukaiFourfold(ideal(x_6-x_7, x_5, x_3-x_4, x_1, x_0-x_4, x_2*x_7-x_4*x_8), ideal(x_4*x_6-x_3*x_7+x_1*x_8, x_4*x_5-x_2*x_7+x_0*x_8, x_3*x_5-x_2*x_6+x_0*x_8+x_1*x_8-x_5*x_8, x_1*x_5-x_0*x_6+x_0*x_7+x_1*x_7-x_5*x_7, x_1*x_2-x_0*x_3+x_0*x_4+x_1*x_4-x_2*x_7+x_0*x_8, x_0^2+x_0*x_1+x_1^2+x_0*x_2+2*x_0*x_3+x_1*x_3+x_2*x_3+x_3^2-x_0*x_4-x_1*x_4-2*x_2*x_4-x_3*x_4-2*x_4^2+x_0*x_5+x_2*x_5+x_5^2+2*x_0*x_6+x_1*x_6+2*x_2*x_6+x_3*x_6+x_5*x_6+x_6^2-3*x_4*x_7+2*x_5*x_7-x_7^2+x_1*x_8+x_3*x_8-3*x_4*x_8+2*x_5*x_8+x_6*x_8-x_7*x_8));
-- used 2.69086 seconds
o2 : SpecialGushelMukaiFourfold (Gushel-Mukai fourfold containing a surface of degree 2 and sectional genus 0)
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i3 : time toGrass X
-- used 2.79394 seconds
o3 = -- rational map --
ZZ
source: subvariety of Proj(-----[x , x , x , x , x , x , x , x , x ]) defined by
33331 0 1 2 3 4 5 6 7 8
{
x x - x x + x x ,
4 6 3 7 1 8
x x - x x + x x ,
4 5 2 7 0 8
x x - x x + x x + x x - x x ,
3 5 2 6 0 8 1 8 5 8
x x - x x + x x + x x - x x ,
1 5 0 6 0 7 1 7 5 7
x x - x x + x x + x x - x x + x x ,
1 2 0 3 0 4 1 4 2 7 0 8
2 2 2 2 2 2 2
x + x x + x + x x + 2x x + x x + x x + x - x x - x x - 2x x - x x - 2x + x x + x x + x + 2x x + x x + 2x x + x x + x x + x - 3x x + 2x x - x + x x + x x - 3x x + 2x x + x x - x x
0 0 1 1 0 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 2 5 5 0 6 1 6 2 6 3 6 5 6 6 4 7 5 7 7 1 8 3 8 4 8 5 8 6 8 7 8
}
ZZ
target: subvariety of Proj(-----[t , t , t , t , t , t , t , t , t , t ]) defined by
33331 0,1 0,2 1,2 0,3 1,3 2,3 0,4 1,4 2,4 3,4
{
t t - t t + t t ,
2,3 1,4 1,3 2,4 1,2 3,4
t t - t t + t t ,
2,3 0,4 0,3 2,4 0,2 3,4
t t - t t + t t ,
1,3 0,4 0,3 1,4 0,1 3,4
t t - t t + t t ,
1,2 0,4 0,2 1,4 0,1 2,4
t t - t t + t t
1,2 0,3 0,2 1,3 0,1 2,3
}
defining forms: {
- 7845x + 1525x + 1237x - 8266x + 13726x - 2723x - 11367x + 6823x + 5507x ,
0 1 2 3 4 5 6 7 8
- 2809x + 15639x - 3701x + 1862x + 13010x + 2558x - 14802x + 7843x - 9490x ,
0 1 2 3 4 5 6 7 8
901x - 7265x - 4798x - 14457x + 14623x - 4796x + 6045x - 11919x + 9036x ,
0 1 2 3 4 5 6 7 8
11319x - 55x - 4501x - 3631x - 5252x - 14495x - 9043x - 2551x + 14859x ,
0 1 2 3 4 5 6 7 8
14663x + 1607x + 7807x + 1693x + 9805x + 15730x - 3322x - 14632x + 12855x ,
0 1 2 3 4 5 6 7 8
10646x + 13311x - 10961x + 6949x + 13932x - 16629x - 9047x - 16034x + 7382x ,
0 1 2 3 4 5 6 7 8
- 2182x + 10214x - 7890x + 9597x - 3265x - 6753x + 9272x - 3031x - 2487x ,
0 1 2 3 4 5 6 7 8
- 2114x + 8258x - 11200x + 9548x + 922x - 12524x - 3024x + 3031x + 2811x ,
0 1 2 3 4 5 6 7 8
13472x - 12262x + 13792x + 4117x - 14421x + 13781x - 14718x - 1415x - 13177x ,
0 1 2 3 4 5 6 7 8
- 1708x + 8566x - 12166x + 2196x - 11772x + 8441x - 2409x + 13358x + 15575x
0 1 2 3 4 5 6 7 8
}
o3 : RationalMap (linear rational map from 4-dimensional subvariety of PP^8 to 6-dimensional subvariety of PP^9)
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