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OldToricVectorBundles :: cokernel(ToricVectorBundleKlyachko,Matrix)

cokernel(ToricVectorBundleKlyachko,Matrix) -- the cokernel of a morphism to a vector bundle

Synopsis

Description

M must be a matrix over ZZ or QQ where the target space is the space of the bundle, i.e., the matrix must have $k$ rows if the bundle has rank $k$. Then the new bundle is given on each ray $\rho$ by the following filtration of coker(E,M)${}^\rho = ( E^{\rho} ) / $im(M) :

coker(E,M)${}^\rho(i) := E^{\rho}(i) / ( E^{\rho}(i) \cap $ im(M) ).

i1 : E = tangentBundle 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 : E = E ** E

o2 = {dimension of the variety => 2 }
      number of affine charts => 4
      number of rays => 4
      rank of the vector bundle => 4

o2 : ToricVectorBundleKlyachko
i3 : M = matrix {{1,0},{0,1},{1,0},{0,1/1}}

o3 = | 1 0 |
     | 0 1 |
     | 1 0 |
     | 0 1 |

              4        2
o3 : Matrix QQ  <--- QQ
i4 : E1 = coker(E,M)

o4 = {dimension of the variety => 2 }
      number of affine charts => 4
      number of rays => 4
      rank of the vector bundle => 2

o4 : ToricVectorBundleKlyachko
i5 : details E1

o5 = HashTable{| -1 | => (| -1/2 1/2 |, | -2 -1 |)}
               | 2  |     | 1    0   |
               | 0  | => (| 0 1 |, | -2 -1 |)
               | -1 |     | 1 0 |
               | 0 | => (| 0 1 |, | -2 -1 |)
               | 1 |     | 1 0 |
               | 1 | => (| 1 0 |, | -2 -1 |)
               | 0 |     | 0 1 |

o5 : HashTable

See also