isGeneral -- checks whether a toric vector bundle is general

Synopsis

• Usage:

  b = isGeneral E

• Inputs:
  • E, a vector bundle on a toric variety (Klyachko's description)
• Outputs:
  • b, a Boolean value, 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