hh^ZZ ToricVectorBundle -- the rank of the i-th cohomology group of a toric vector bundle

Synopsis

• Scripted functor: hh

• Usage:

  d = hh^i E

  d = hh^i (E,u)

• Inputs:
  • i, an integer
  • E, an instance of the type ToricVectorBundle, and an optional u, a matrix over ZZ, giving a point in the lattice of the fan
• Outputs:
  • d, an integer

Description

i1 : E = tangentBundle hirzebruchFan 2

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

o1 : ToricVectorBundleKlyachko

i2 : u = matrix{{0},{0}}

o2 = 0

              2       1
o2 : Matrix ZZ  <-- ZZ

i3 : hh^0 (E,u)

o3 = 2

i4 : hh^0 E

o4 = 7

See also

• 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,List) -- the i-th cohomology of a toric vector bundle for a given list of degrees
• deltaE -- the polytope of possible degrees that give non zero cohomology