isDegenerate(NormalToricVariety) -- whether a toric variety is degenerate

Synopsis

Function: isDegenerate
Usage:

isDegenerate X
Inputs:
- X, a normal toric variety,
Outputs:
- a Boolean value, that is true if the fan of X is contained in a proper linear subspace of its ambient space

Description

A $d$-dimensional normal toric variety is degenerate if its rays do not span $\QQ^d$. For example, projective spaces and Hirzebruch surfaces are not degenerate.

i1 : assert not isDegenerate toricProjectiveSpace 3

i2 : assert not isDegenerate hirzebruchSurface 7

Although one typically works with non-degenerate toric varieties, not all normal toric varieties are non-degenerate.

i3 : U = normalToricVariety ({{4,-1,0},{0,1,0}},{{0,1}});

i4 : isDegenerate U

o4 = true

Caveat

Many routines in this package, such as the total coordinate ring, require the normal toric variety to be non-degenerate.

Ways to use this method: