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SpecialFanoFourfolds :: toGrass

toGrass -- Gushel morphism from a GM fourfold to Grass(1,4)

Synopsis

Description

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)

See also

Ways to use toGrass :

For the programmer

The object toGrass is a method function.