Collapsing the remaining Gm2 action, the result is a 5-dimensional anti-canonical hypersurface in a toric variety which is birational with F(Q)//Gm3.
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 , s , t , t , r , r , r , r ] 0 1 2 0 1 0 1 2 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 |