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

## Synopsis

• Function: cohomology
• Usage:
c = HH_i^E u
• Inputs:
• Optional inputs:
• Degree (missing documentation) => ..., default value 0,
• Outputs:
• c,

## 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}}