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NormalToricVarieties :: isDegenerate(NormalToricVariety)

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

Synopsis

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.

See also