i1 : P8 = ZZ/33331[x_0..x_8]; |
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 2.34203 seconds o2 : SpecialGushelMukaiFourfold (Gushel-Mukai fourfold containing a surface of degree 2 and sectional genus 0) |
i3 : time toGrass X -- used 2.31632 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) |
The object toGrass is a method function.