Variety -- the class of all algebraic varieties

Types of variety:

• AffineVariety -- the class of all affine varieties
• ProjectiveVariety -- the class of all projective varieties

Functions and methods returning a variety:

• variety -- see variety(CoherentSheaf) -- the underlying variety over which a coherent sheaf or morphism is defined.
• variety(SheafMap) -- see variety(CoherentSheaf) -- the underlying variety over which a coherent sheaf or morphism is defined.

Methods that use a variety:

• codim(Variety) -- codimension of a variety
• expression(Variety) (missing documentation)
• HH^ZZ(Variety,SheafOfRings) (missing documentation)
• ideal(Variety) -- returns the defining ideal
• isProjective(Variety) -- see isProjective -- whether a variety is projective
• isSmooth(Variety) -- whether a variety is smooth
• isWellDefined(Variety) -- whether a variety is well-defined
• mathML(Variety) (missing documentation)
• net(Variety) (missing documentation)
• ring(Variety) -- coordinate ring of the variety
• sheaf(Variety,Matrix) -- see sheaf(Matrix) -- the sheafification functor for morphisms
• sheaf(Variety,Matrix,ZZ) -- see sheaf(Matrix) -- the sheafification functor for morphisms
• sheaf(Variety) -- make a coherent sheaf
• sheaf(Variety,Ideal) -- see sheaf(Variety,Module) -- make a coherent sheaf
• sheaf(Variety,Module) -- make a coherent sheaf
• sheaf(Variety,Ring) -- make a coherent sheaf of rings
• texMath(Variety) (missing documentation)
• toExternalString(Variety) (missing documentation)
• toString(Variety) (missing documentation)

For the programmer

The object Variety is a type, with ancestor classes MutableHashTable < HashTable < Thing.

The source of this document is in Varieties/doc-varieties.m2:15:0.