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

Synopsis

Function: variety
Usage:

variety A
Inputs:
- A, 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:
- $X$, the variety associated with A, or with the ring of A, if A is a RingElement

Description

i1 : needsPackage "NormalToricVarieties"

o1 = NormalToricVarieties

o1 : Package

i2 : X = toricProjectiveSpace 1

o2 = X

o2 : NormalToricVariety

i3 : S = ring X
warning: clearing value of symbol x to allow access to subscripted variables based on it
       : debug with expression   debug 9868   or with command line option   --debug 9868

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

If a RingElement is provided, then the variety of its ring is returned.

i9 : variety S_0

o9 = X

o9 : NormalToricVariety

i10 : variety IY_0

o10 = Y

o10 : a flag bundle with subquotient ranks {2:1}

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

Ways to use this method: