isSmooth(Variety) -- whether a variety is smooth

Function: isSmooth
Usage:

isSmooth X
Inputs:
- X, a variety,
Outputs:
- a Boolean value,

Description

An affine variety $X$ is smooth if the singular locus of $X$ is empty, while a projective variety is smooth if the singular locus is supported at the origin.

i1 : R = quotient minors_2 genericMatrix(QQ[x,y,z,w], 2, 2)

o1 = R

o1 : QuotientRing

i2 : isSmooth Proj R

o2 = true

i3 : isSmooth Spec R

o3 = false

Ways to use this method:

isSmooth(Variety) -- whether a variety is smooth

The source of this document is in Varieties/doc-varieties.m2:362:0.

isSmooth(Variety) -- whether a variety is smooth

Description

See also

Ways to use this method: