i2 : 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));
o2 : ProjectiveVariety, GM fourfold containing a surface of degree 2 and sectional genus 0
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i4 : show oo
o4 = -- multi-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(-----[x , x , x , x , x , x , x , x , x , x ]) defined by
33331 0,1 0,2 1,2 0,3 1,3 2,3 0,4 1,4 2,4 3,4
{
x x - x x + x x ,
2,3 1,4 1,3 2,4 1,2 3,4
x x - x x + x x ,
2,3 0,4 0,3 2,4 0,2 3,4
x x - x x + x x ,
1,3 0,4 0,3 1,4 0,1 3,4
x x - x x + x x ,
1,2 0,4 0,2 1,4 0,1 2,4
x x - x x + x x
1,2 0,3 0,2 1,3 0,1 2,3
}
-- rational map 1/1 --
map 1/1, one of its representatives:
{
5418x - 821x + 5588x - 3585x - 1758x - 15576x + 9147x - 14993x - 4736x ,
0 1 2 3 4 5 6 7 8
11632x - 4732x - 10523x - 11526x - 1991x - 1831x - 9701x + 12320x - 2015x ,
0 1 2 3 4 5 6 7 8
16371x - 7244x + 4935x + 15111x + 3749x - 12977x + 15511x + 7287x + 6751x ,
0 1 2 3 4 5 6 7 8
- 13960x - 3219x + 8239x - 10597x + 7747x + 273x - 6285x + 2934x - 4471x ,
0 1 2 3 4 5 6 7 8
- 12638x - 12017x - 2651x + 7012x - 9505x + 3559x - 2170x - 59x - 265x ,
0 1 2 3 4 5 6 7 8
- 4096x + 10456x - 2284x + 11208x + 5756x - 6263x + 599x + 7817x - 6486x ,
0 1 2 3 4 5 6 7 8
5896x + 11711x - 9239x + 9726x + 9682x + 2295x - 6875x - 16024x - 7246x ,
0 1 2 3 4 5 6 7 8
- 8687x + 14564x + 3651x - 6141x - 7924x + 3227x - 5479x + 13427x + 11982x ,
0 1 2 3 4 5 6 7 8
89x + 11710x + 1284x - 12079x + 11673x - 2256x + 12732x - 7459x - 5231x ,
0 1 2 3 4 5 6 7 8
- 25x + 12923x + 1000x + 871x + 15902x - 3782x - 7479x - 5250x + 11717x
0 1 2 3 4 5 6 7 8
}
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