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ToricVectorBundles :: regCheck

regCheck -- checking the regularity condition for a toric vector bundle

Synopsis

Description

"For a toric vector bundle in Kaneyama’s description, the regularity condition means that for every pair of maximal cones σ12intersecting in a common codimension-one face, the two sets of degrees d1,d2 and the transition matrix A1,2 fulfil the regularity condition. I.e. for every i and j we have that either the (i,j) entry of the matrix A1,2 is 0 or the difference of the i-th degree vector of d1 of σ1 and the j-th degree vector of d2 of σ2 is in the dual cone of the intersection of σ1 and σ2."

Note that this is only necessary for toric vector bundles generated 'by hand' using addBaseChange and addDegrees, since bundles generated for example by tangentBundle satisfy the condition autmatically.

i1 : E = tangentBundle(pp1ProductFan 2,"Type" => "Kaneyama")

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

o1 : ToricVectorBundleKaneyama
i2 : regCheck E

o2 = true

See also

Ways to use regCheck :