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NumericalGodeaux :: modelInP1BundleOverP2xP5

modelInP1BundleOverP2xP5 -- compute the projection from a double point of H_{4,6}

Synopsis

Usage:
G= modelInP1BundleOverP2xP5(H)
Inputs:
- H, a matrix, defining the hypersurface in P3xP5
Outputs:
- G, a matrix, of the equation of a hypersurface

Description

The hypersurface H_4,6 ⊂ℙ³ ×ℙ⁵ is singular along (0,0,0,1) ×ℙ⁵. The function describes H_4,6 via the projection from this point.

i1 : H = precomputedModelInP3xP5(QQ);

                                                        1                                                  1
o1 : Matrix (QQ[w , w , w , w , z , z , z , z , z , z ])  <--- (QQ[w , w , w , w , z , z , z , z , z , z ])
                 0   1   2   3   0   1   2   3   4   5              0   1   2   3   0   1   2   3   4   5

i2 : G = ideal modelInP1BundleOverP2xP5(H);

o2 : Ideal of QQ[x , x , y , y , y , z , z , z , z , z , z ]
                  0   1   0   1   2   0   1   2   3   4   5

i3 : 7==dim  G-3

o3 = true

i4 : sum degrees ring G

o4 = {2, 4, 6}

o4 : List

i5 : degrees source gens G

o5 = {{2, 4, 6}}

o5 : List

See also

findPointInP3xP5 -- find a point on the model in P3xP5

Ways to use `modelInP1BundleOverP2xP5` :

modelInP1BundleOverP2xP5(Matrix)