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

Synopsis

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

Description

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

For package developers: All this function does is to look up the symbol variety in S. This is currently used in two packages, but can be used in other settings, if desired.

Code

../../../../../Macaulay2/packages/Varieties.m2:209:19-209:56: --source code:
variety Ring  := S -> if S.?variety then S.variety else error "no variety associated with ring"

Ways to use this method: