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NumericalGodeaux :: collapsingOneCStar

collapsingOneCStar -- compute the hypersurface of bidegree (4,6) in P3xP5

Synopsis

Description

The function computes a hypersurface $H_{4,6}$ of bidegree $(4,6)$ in $\mathbb{P}^3 \times \mathbb{P}^5$ which is the image of the model of $F(Q)$ in $\mathbb{P}^3 \times \mathbb{P}^3 \times \mathbb{P}^3 \times \mathbb{P}^3$ under a rational map. The fibers of the map are $G_m$-orbits.

i1 : kk = QQ

o1 = QQ

o1 : Ring
 
i2 : I1=precomputedModelInP3xP3xP3xP3(kk);

o2 : Ideal of QQ[b   ..b   ]
                  0,0   3,3
 
i3 : isHomogeneous I1

o3 = true
 
i4 : "--H=collapsingOneCStar I1;"

o4 = --H=collapsingOneCStar I1;

Since the function takes about 150 secends we use the precomputed equations.

i5 : H = precomputedModelInP3xP5(QQ);

                                1                          1
o5 : Matrix (QQ[w ..w , z ..z ])  <--- (QQ[w ..w , z ..z ])
                 0   3   0   5              0   3   0   5
 
i6 : degrees  ring H

o6 = {{1, 0}, {1, 0}, {1, 0}, {1, 0}, {0, 1}, {0, 1}, {0, 1}, {0, 1}, {0, 1},
     ------------------------------------------------------------------------
     {0, 1}}

o6 : List
 
i7 : degrees source H

o7 = {{4, 6}}

o7 : List
 
i8 : sum degrees ring H

o8 = {4, 6}

o8 : List
 
i9 : betti H

            0 1
o9 = total: 1 1
         0: 1 .
         1: . .
         2: . .
         3: . .
         4: . .
         5: . .
         6: . .
         7: . .
         8: . .
         9: . 1

o9 : BettiTally
 
i10 : tH=terms H_(0,0);
 
i11 : #tH

o11 = 128
 
i12 : lcmTH=lcm tH

                     3 2 4 2 3 3 3 3 3 3
o12 = 13209037701120w w w w z z z z z z
                     0 1 2 3 0 1 2 3 4 5

o12 : QQ[w ..w , z ..z ]
          0   3   0   5
 
i13 : factor sub((coefficients lcmTH)_1_(0,0),ZZ)

       27 9
o13 = 2  3 5

o13 : Expression of class Product

See also

Ways to use collapsingOneCStar :

For the programmer

The object collapsingOneCStar is a method function.