next | previous | forward | backward | up | top | index | toc | Macaulay2 website
NumericalGodeaux :: furtherCollapsing

furtherCollapsing -- computes the 5-dimensional anti-canonical hypersurface in the cox ring of a toric variety

Synopsis

Description

Collapsing the remaining $G_m^2$ action, the result is a 5-dimensional anti-canonical hypersurface in a toric variety which is birational with $F(Q)//G_m^3$.

i1 : "--elapsedTime G = furtherCollapsing(QQ);"

o1 = --elapsedTime G = furtherCollapsing(QQ);

Since the computation of the model takes some time, we use the pre-computed model. The toric variety is a P3-bundle over a P2-bundle over P1.

i2 : G= precomputedCoxModel(QQ);

o2 : Ideal of QQ[s ..s , t ..t , r ..r ]
                  0   2   0   1   0   3
 
i3 : coxRing = ring G

o3 = coxRing

o3 : PolynomialRing
 
i4 : 5==dim G-3

o4 = true
 
i5 : degrees coxRing

o5 = {{1, 1, 0}, {1, 1, 0}, {1, 0, 0}, {0, 1, 0}, {0, 1, 0}, {1, 2, 1}, {1,
     ------------------------------------------------------------------------
     2, 1}, {1, 2, 1}, {0, 0, 1}}

o5 : List
 
i6 : degrees source gens G

o6 = {{6, 10, 4}}

o6 : List
 
i7 : sum degrees coxRing

o7 = {6, 10, 4}

o7 : List
 
i8 : tG=terms G_0;
 
i9 : #tG

o9 = 128
 
i10 : lcmTG=lcm tG

                     3 3 2 2 4 3 3 2 2
o10 = 13209037701120s s s t t r r r r
                     0 1 2 0 1 0 1 2 3

o10 : coxRing
 
i11 : factor sub((coefficients lcmTG)_1_(0,0),ZZ)

       27 9
o11 = 2  3 5

o11 : Expression of class Product

See also

Ways to use furtherCollapsing :

For the programmer

The object furtherCollapsing is a method function.