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OldToricVectorBundles :: deltaE

deltaE -- the polytope of possible degrees that give non zero cohomology

Synopsis

Description

For a toric vector bundle over a complete toric variety there is a finite set of degrees $u$ such that the degree $u$ part of the cohomology of the vector bundle is non-zero. This function computes a polytope $\Delta_E$, such that these degrees are contained in this polytope. If the underlying toric variety is not complete then an error is returned.

i1 : E = toricVectorBundle(2,pp1ProductFan 2, "Type" => "Kaneyama")

o1 = {dimension of the variety => 2 }
      number of affine charts => 4
      rank of the vector bundle => 2

o1 : ToricVectorBundleKaneyama
i2 : P = deltaE E

o2 = {ambient dimension => 2           }
      dimension of lineality space => 0
      dimension of polyhedron => 0
      number of facets => 0
      number of rays => 0
      number of vertices => 1

o2 : Polyhedron
i3 : vertices P

o3 = 0

              2        1
o3 : Matrix QQ  <--- QQ
i4 : E1 = tangentBundle projectiveSpaceFan 2

o4 = {dimension of the variety => 2 }
      number of affine charts => 3
      number of rays => 3
      rank of the vector bundle => 2

o4 : ToricVectorBundleKlyachko
i5 : P1 = deltaE E1

o5 = {ambient dimension => 2           }
      dimension of lineality space => 0
      dimension of polyhedron => 2
      number of facets => 6
      number of rays => 0
      number of vertices => 6

o5 : Polyhedron
i6 : vertices P1

o6 = | -1 1 0  1  0 -1 |
     | 0  0 -1 -1 1 1  |

              2        6
o6 : Matrix QQ  <--- QQ

See also

Ways to use deltaE :

For the programmer

The object deltaE is a method function.