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ToricVectorBundles :: HH^ZZ(ToricVectorBundle,Matrix)

HH^ZZ(ToricVectorBundle,Matrix) -- the i-th cohomology of a toric vector bundle in a given degree

Synopsis

Description

"Computes the $i$-th cohomology group of the toric vector bundle $E$ of degree $u$ where $u$ must be a one-column matrix giving a point in the lattice of the fan over which $E$ is defined and $i$ must be between $0$ and the dimension of the underlying toric variety."

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}})

           1
o2 = (QQ[])

o2 : QQ[]-module, free, degrees {{1, 0}}

See also