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4 Toric subvarieties
 4.1 The GAP category
 4.2 Properties
 4.3 Attributes
 4.4 Methods
 4.5 Constructors

4 Toric subvarieties

4.1 The GAP category

4.1-1 IsToricSubvariety
‣ IsToricSubvariety( M )( filter )

Returns: true or false

The GAP category of a toric subvariety. Every toric subvariety is a toric variety, so every method applicable to toric varieties is also applicable to toric subvarieties.

4.2 Properties

4.2-1 IsClosedSubvariety
‣ IsClosedSubvariety( vari )( property )

Returns: true or false

Checks if the subvariety vari is a closed subset of its ambient variety.

4.2-2 IsOpen
‣ IsOpen( vari )( property )

Returns: true or false

Checks if a subvariety is a closed subset.

4.2-3 IsWholeVariety
‣ IsWholeVariety( vari )( property )

Returns: true or false

Returns true if the subvariety vari is the whole variety.

4.3 Attributes

4.3-1 UnderlyingToricVariety
‣ UnderlyingToricVariety( vari )( attribute )

Returns: a variety

Returns the toric variety which is represented by vari. This method implements the forgetful functor subvarieties -> varieties.

4.3-2 InclusionMorphism
‣ InclusionMorphism( vari )( attribute )

Returns: a morphism

If the variety vari is an open subvariety, this method returns the inclusion morphism in its ambient variety. If not, it will fail.

4.3-3 AmbientToricVariety
‣ AmbientToricVariety( vari )( attribute )

Returns: a variety

Returns the ambient toric variety of the subvariety vari

4.4 Methods

4.4-1 ClosureOfTorusOrbitOfCone
‣ ClosureOfTorusOrbitOfCone( vari, cone )( operation )

Returns: a subvariety

The method returns the closure of the orbit of the torus contained in vari which corresponds to the cone cone as a closed subvariety of vari.

4.5 Constructors

4.5-1 ToricSubvariety
‣ ToricSubvariety( vari, ambvari )( operation )

Returns: a subvariety

The method returns the closure of the orbit of the torus contained in vari which corresponds to the cone cone as a closed subvariety of vari.

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