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findWeights -- finds the possible weight vectors for the maximal cones

Description

The list L contains a list for each maximal cone $\sigma$ of the underlying fan. For each maximal cone $\sigma$ this list contains all matrices of possible weight vectors, that induce the filtrations on the rays of this cone (modulo permutations, but yet not all permutations). This means that for one of these matrices $M$ multiplied with the matrix $R$ of rays of this cone (the rays are the rows) gives the matrix of filtrations of these rays (where for each filtration the entries may be permuted). 
i1 : E = tangentBundle projectiveSpaceFan 3

o1 = {dimension of the variety => 3 }
      number of affine charts => 4
      number of rays => 4
      rank of the vector bundle => 3

o1 : ToricVectorBundleKlyachko
 
i2 : findWeights E

o2 = {{| 1  1 1  |, | 1  1  1 |}, {| -1 0 0  |, | -1 0  0 |}, {| -1 0  0  |,
       | -1 0 0  |  | -1 0  0 |    | 1  1 1  |  | 1  1  1 |    | 0  -1 0  | 
       | 0  0 -1 |  | 0  -1 0 |    | 0  0 -1 |  | 0  -1 0 |    | 0  0  -1 | 
     ------------------------------------------------------------------------
     | -1 0  0  |}, {| -1 0  0 |, | -1 0 0  |}}
     | 0  0  -1 |    | 0  -1 0 |  | 0  0 -1 |
     | 0  -1 0  |    | 1  1  1 |  | 1  1 1  |

o2 : List

See also

Ways to use findWeights:

  • findWeights(ToricVectorBundleKlyachko)

For the programmer

The object findWeights is a method function.

The source of this document is in ToricVectorBundles.m2:2998:0.