Macaulay2 » Documentation
Packages » OldToricVectorBundles :: base
next | previous | forward | backward | up | index | toc

# base -- the basis matrices for the rays

- Usage:
    `b = base E`
- Inputs:
  - E, a vector bundle on a toric variety (Klyachko's description)
- Outputs:
  - b, a hash table

## Description

The basis of a toric vector bundle in Klyachko's description is given for each ray as a square matrix of rank $k$ of the bundle. The output is a HashTable where the keys are the rays of the fan given as one column matrices over ZZ, and for each ray a $k$ by $k$ matrix over QQ and $k$ is the rank of the bundle.

    i1 : E = tangentBundle hirzebruchFan 3

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

    o1 : ToricVectorBundleKlyachko

    i2 : base E

    o2 = HashTable{| -1 | => | -1 1/3 |}
                   | 3  |    | 3  0   |
                   | 0  | => | 0  1 |
                   | -1 |    | -1 0 |
                   | 0 | => | 0 1 |
                   | 1 |    | 1 0 |
                   | 1 | => | 1 0 |
                   | 0 |    | 0 1 |

    o2 : HashTable

## See also

- addBase -- changing the basis matrices of a toric vector bundle in Klyachko's description
- filtration -- the filtration matrices of the vector bundle
- isVectorBundle -- checks if the data does in fact define an equivariant toric vector bundle

## Ways to use base:

- `base(ToricVectorBundleKlyachko)`

## For the programmer

The object base is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/OldToricVectorBundles.m2:2392:0.