HH^ZZ(ToricVectorBundle,List) -- the i-th cohomology of a toric vector bundle for a given list of degrees

Synopsis

• Function: cohomology

• Usage:

  c = HH_i^E L

• Inputs:
  • i, an integer
  • E, an instance of the type ToricVectorBundle
  • L, a list, containing weights of the form, one column matrix over ZZ
• Optional inputs:
  • Degree (missing documentation) => ..., default value 0,
• Outputs:
  • c, a list

Description

i1 : E = tangentBundle hirzebruchFan 3

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

o1 : ToricVectorBundleKlyachko

i2 : HH_0^E {matrix{{1},{0}},matrix{{-1},{0}}}

            1        1
o2 = {(QQ[]) , (QQ[]) }

o2 : List

See also

• ring(ToricVectorBundle) -- the graded ring of the bundle
• deltaE -- the polytope of possible degrees that give non zero cohomology
• HH^ZZ ToricVectorBundle -- the i-th cohomology group of a toric vector bundle
• HH^ZZ(ToricVectorBundle,Matrix) -- the i-th cohomology of a toric vector bundle in a given degree
• hh^ZZ ToricVectorBundle
• eulerChi -- the Euler characteristic of a toric vector bundle