next | previous | forward | backward | up | top | index | toc | Macaulay2 website
ToricVectorBundles :: ring(ToricVectorBundle)

ring(ToricVectorBundle) -- the graded ring of the bundle

Synopsis

Description

For a vector bundle in Kaneyama's description the graded ring is QQ with degree space the lattice of the underlying fan.

i1 : E = tangentBundle(projectiveSpaceFan 3,"Type" => "Kaneyama")

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

o1 : ToricVectorBundleKaneyama
i2 : ring E

o2 = QQ[]

o2 : PolynomialRing

For a vector bundle in Klyachko's description the graded ring is QQ with degree space the lattice of the underlying fan.

i3 : E = toricVectorBundle(1,projectiveSpaceFan 2, toList(3:matrix{{1/2}}),toList(3:matrix{{-1}}))

o3 = {dimension of the variety => 2 }
      number of affine charts => 3
      number of rays => 3
      rank of the vector bundle => 1

o3 : ToricVectorBundleKlyachko
i4 : ring E

o4 = QQ[]

o4 : PolynomialRing

See also