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 1.79983 seconds
o2 : SpecialGushelMukaiFourfold (Gushel-Mukai fourfold containing a surface of degree 2 and sectional genus 0)
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i3 : time embed X
-- used 4.155e-6 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: {
- 9249x + 3767x + 164x - 6955x - 13415x + 5189x - 9034x + 1398x + 6379x ,
0 1 2 3 4 5 6 7 8
- 9037x + 15555x + 13722x + 7428x - 1280x - 12690x + 101x - 124x - 1300x ,
0 1 2 3 4 5 6 7 8
5752x + 10216x + 6915x - 9854x + 5406x + 4875x + 242x + 5553x - 3485x ,
0 1 2 3 4 5 6 7 8
- 13975x + 2023x + 11207x - 15085x + 5060x + 15069x - 7126x + 14018x + 12225x ,
0 1 2 3 4 5 6 7 8
- 730x + 5597x - 5903x + 15684x + 1908x + 2809x + 1043x + 15326x + 9438x ,
0 1 2 3 4 5 6 7 8
- 6716x + 7618x - 2084x + 1301x - 1630x - 7544x - 5283x - 5208x - 1196x ,
0 1 2 3 4 5 6 7 8
- 5177x + 16076x + 4914x - 13188x - 8068x - 15760x + 15536x - 6172x + 3400x ,
0 1 2 3 4 5 6 7 8
492x + 12248x - 6423x + 16363x + 7703x - 6141x + 8379x + 3553x - 10525x ,
0 1 2 3 4 5 6 7 8
4274x + 554x + 3301x + 16195x - 16199x + 14479x + 12627x - 3599x + 15273x ,
0 1 2 3 4 5 6 7 8
- 10607x + 1565x - 8200x + 5233x + 1920x - 10028x + 9532x - 9674x - 11506x
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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