# isGeneral -- checks whether a toric vector bundle is general

## Synopsis

• Usage:
b = isGeneral E
• Inputs:
• Outputs:
• b, , whether E is general

## Description

"A toric vector bundle in Klyachko's description is general if for every maximal cone $\Sigma$ in the fan the following condition holds: Let $\rho_1,...,\rho_l$ be the rays of $\sigma$. Then for every choice of filtration steps $i_1,...,i_l$ for each ray, i.e., choose an integer for each ray where the filtration enlarges, the equation"

codim $(\cap E^{\rho_j} ( i_j )) = min \{ \sum ($codim $E^{\rho_j} ( i_j )),rank E \}$

holds.

 i1 : E = cotangentBundle 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 : isGeneral E o2 = true

## See also

• filtration -- the filtration matrices of the vector bundle
• base -- the basis matrices for the rays
• randomDeformation -- a random deformation of a given toric vector bundle

## Ways to use isGeneral :

• "isGeneral(ToricVectorBundleKlyachko)"

## For the programmer

The object isGeneral is .