variety(Ring) -- the variety previously associated to a given ring

• Function: variety

• Usage:

  variety S

• Inputs:
  • S, a ring, the intersection ring of a variety $X$, say, or the homogeneous (Cox) ring of a normal toric variety, or another ring that has been associated to a variety, or an element in such a ring
• Outputs:
  • a variety, $X$, the variety associated with S

i1 : needsPackage "NormalToricVarieties"

o1 = NormalToricVarieties

o1 : Package

i2 : X = toricProjectiveSpace 1

o2 = X

o2 : NormalToricVariety

i3 : S = ring X

o3 = S

o3 : PolynomialRing

i4 : X === variety S

o4 = true

i5 : needsPackage "Schubert2"

o5 = Schubert2

o5 : Package

i6 : Y = abstractProjectiveSpace 1

o6 = Y

o6 : a flag bundle with subquotient ranks {2:1}

i7 : IY = intersectionRing Y

o7 = IY

o7 : QuotientRing

i8 : Y === variety IY

o8 = true

../../../../Macaulay2/packages/Varieties.m2:220:17-220:62: --source code:
variety Ring  := S -> if S.?variety then S.variety else Proj S