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ToricVectorBundles :: addDegrees

addDegrees -- changing the degrees of a toric vector bundle

Synopsis

Description

addDegrees replaces the degree matrices in E by the matrices in the List L. The matrices in L must be $n$ by $k$ matrices over ZZ, where $k$ is the rank of the vector bundle E and $n$ is the dimension of the underlying toric variety. The list has to contain one matrix for each maximal dimensional cone of the underlying fan over which E is defined. Note that in E the top dimensional cones are already sorted and that the degree matrices in L will be assigned to the cones in that order. To find out the order use maxCones(ToricVectorBundle). The matrices need not satisfy the regularity condition. This can be checked with regCheck. 

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

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

o1 : ToricVectorBundleKaneyama
 
i2 : details E

o2 = (HashTable{0 => (| 1 0 |, 0)  }, HashTable{(0, 1) => | 1 0 |})
                      | 0 1 |                             | 0 1 |
                1 => (| 1 0  |, 0)              (0, 2) => | 1 0 |
                      | 0 -1 |                            | 0 1 |
                2 => (| -1 0 |, 0)              (1, 3) => | 1 0 |
                      | 0  1 |                            | 0 1 |
                3 => (| -1 0  |, 0)             (2, 3) => | 1 0 |
                      | 0  -1 |                           | 0 1 |

o2 : Sequence
 
i3 : F = addDegrees(E,{matrix{{1,2},{3,1}},matrix{{-1,0},{3,1}},matrix{{1,2},{-3,-1}},matrix{{-1,0},{-3,-1}}})

o3 = {dimension of the variety => 2 }
      number of affine charts => 4
      rank of the vector bundle => 2

o3 : ToricVectorBundleKaneyama
 
i4 : details F

o4 = (HashTable{0 => (| 1 0 |, | 1 2 |)    }, HashTable{(0, 1) => | 1 0 |})
                      | 0 1 |  | 3 1 |                            | 0 1 |
                1 => (| 1 0  |, | -1 0 |)               (0, 2) => | 1 0 |
                      | 0 -1 |  | 3  1 |                          | 0 1 |
                2 => (| -1 0 |, | 1  2  |)              (1, 3) => | 1 0 |
                      | 0  1 |  | -3 -1 |                         | 0 1 |
                3 => (| -1 0  |, | -1 0  |)             (2, 3) => | 1 0 |
                      | 0  -1 |  | -3 -1 |                        | 0 1 |

o4 : Sequence
 
i5 : regCheck F

o5 = false

See also

Ways to use addDegrees :

For the programmer

The object addDegrees is a method function.