next | previous | forward | backward | up | top | index | toc | Macaulay2 website
ToricVectorBundles :: isomorphism

isomorphism -- the isomorphism if the two bundles are isomorphic

Synopsis

Description

Two equivariant vector bundles in Klyachko's description are isomorphic if there exists a simultaneous isomorphism for the filtered vector spaces of all rays. If the two bundles are isomorphic (see areIsomorphic) this function returns the isomorphism. For this, the two bundles must be defined over the same fan.

i1 : HF = hirzebruchFan 2

o1 = HF

o1 : Fan
i2 : E = exteriorPower(2, cotangentBundle HF)

o2 = {dimension of the variety => 2 }
      number of affine charts => 4
      number of rays => 4
      rank of the vector bundle => 1

o2 : ToricVectorBundleKlyachko
i3 : F = weilToCartier({-1,-1,-1,-1},HF)

o3 = {dimension of the variety => 2 }
      number of affine charts => 4
      number of rays => 4
      rank of the vector bundle => 1

o3 : ToricVectorBundleKlyachko
i4 : M = isomorphism(E,F)

o4 = | 1 |

              1        1
o4 : Matrix QQ  <--- QQ

See also

Ways to use isomorphism :

For the programmer

The object isomorphism is a method function.