MultiprojectiveVariety -- the class of all multi-projective varieties

Types of multi-projective variety :

• EmbeddedProjectiveVariety -- the class of all embedded projective varieties
• WeightedProjectiveVariety -- the class of all weighted projective varieties

Functions and methods returning a multi-projective variety :

• ambientVariety -- the ambient variety of a projective subvariety
• baseLocus -- the base locus of a multi-rational map
• fiberProduct -- fiber product of multi-projective varieties
• projectiveVariety -- the closed multi-projective subvariety defined by a multi-homogeneous ideal

Methods that use a multi-projective variety :

• ambient(MultiprojectiveVariety) -- the ambient multi-projective space of the variety
• ambientVariety(MultiprojectiveVariety) -- see ambientVariety -- the ambient variety of a projective subvariety
• codim(MultiprojectiveVariety) -- the codimension of the variety
• coefficientRing(MultiprojectiveVariety) -- the coefficient ring of the variety
• decompose(MultiprojectiveVariety) -- irreducible components of a variety
• degree(MultiprojectiveVariety) -- the degree of the variety
• degrees(MultiprojectiveVariety) -- degrees for the minimal generators
• ? MultiprojectiveVariety -- see describe(MultiprojectiveVariety) -- describe a multi-projective variety
• describe(MultiprojectiveVariety) -- describe a multi-projective variety
• dim(MultiprojectiveVariety) -- the dimension of the variety
• euler(MultiprojectiveVariety) -- topological Euler characteristic of a (smooth) multi-projective variety
• forceImage(MultirationalMap,MultiprojectiveVariety) -- declare which is the image of a multi-rational map
• Hom(MultiprojectiveVariety,MultiprojectiveVariety) -- get the hom-set of rational maps between two multi-projective varieties
• Hom(MultiprojectiveVariety,Nothing) -- see Hom(MultiprojectiveVariety,MultiprojectiveVariety) -- get the hom-set of rational maps between two multi-projective varieties
• Hom(MultiprojectiveVariety,Symbol) -- see Hom(MultiprojectiveVariety,MultiprojectiveVariety) -- get the hom-set of rational maps between two multi-projective varieties
• Hom(Nothing,MultiprojectiveVariety) -- see Hom(MultiprojectiveVariety,MultiprojectiveVariety) -- get the hom-set of rational maps between two multi-projective varieties
• ideal(MultiprojectiveVariety) -- the defining ideal of the variety
• isSubset(MultiprojectiveVariety,MultiprojectiveVariety) -- whether one variety is a subvariety of another
• multidegree(MultiprojectiveVariety) -- the multidegree of the variety
• MultiprojectiveVariety % MultiprojectiveVariety -- subvariety of a projective variety
• MultiprojectiveVariety * MultiprojectiveVariety -- intersection of two multi-projective varieties
• MultiprojectiveVariety ** MultiprojectiveVariety -- product of two multi-projective varieties
• MultiprojectiveVariety ** Ring -- change the coefficient ring of a multi-projective variety
• MultiprojectiveVariety + MultiprojectiveVariety -- union of two multi-projective varieties
• MultiprojectiveVariety == MultiprojectiveVariety -- equality of multi-projective varieties
• MultiprojectiveVariety \ MultiprojectiveVariety -- difference of multi-projective varieties
• MultiprojectiveVariety \\ MultiprojectiveVariety -- difference of multi-projective varieties
• MultiprojectiveVariety ^ ZZ -- power of a multi-projective variety
• multirationalMap(List,MultiprojectiveVariety) -- see multirationalMap -- the multi-rational map defined by a list of rational maps
• MultiprojectiveVariety << MultiprojectiveVariety -- see MultirationalMap << MultiprojectiveVariety -- force the change of the target in a multi-rational map
• MultirationalMap << MultiprojectiveVariety -- force the change of the target in a multi-rational map
• MultirationalMap ^** MultiprojectiveVariety -- inverse image via a multi-rational map
• MultirationalMap | MultiprojectiveVariety -- restriction of a multi-rational map
• RationalMap | MultiprojectiveVariety -- see MultirationalMap | MultiprojectiveVariety -- restriction of a multi-rational map
• MultirationalMap || MultiprojectiveVariety -- restriction of a multi-rational map
• RationalMap || MultiprojectiveVariety -- see MultirationalMap || MultiprojectiveVariety -- restriction of a multi-rational map
• MultirationalMap MultiprojectiveVariety -- direct image via a multi-rational map
• RationalMap MultiprojectiveVariety -- see MultirationalMap MultiprojectiveVariety -- direct image via a multi-rational map
• multirationalMap(MultiprojectiveVariety) -- identity map
• ZZ _ MultiprojectiveVariety -- see multirationalMap(MultiprojectiveVariety) -- identity map
• multirationalMap(MultiprojectiveVariety,MultiprojectiveVariety) -- get the natural inclusion
• rationalMap(MultiprojectiveVariety,MultiprojectiveVariety) -- see multirationalMap(MultiprojectiveVariety,MultiprojectiveVariety) -- get the natural inclusion
• multirationalMap(MultirationalMap,MultiprojectiveVariety) -- change the target of a multi-rational map
• rationalMap(MultirationalMap,MultiprojectiveVariety) -- see multirationalMap(MultirationalMap,MultiprojectiveVariety) -- change the target of a multi-rational map
• parametrize(MultiprojectiveVariety) -- try to get a parametrization of a multi-projective variety
• permute(MultiprojectiveVariety,List) -- permute the factors of the ambient multi-projective space
• |- MultiprojectiveVariety -- see point(MultiprojectiveVariety) -- pick a random rational point on a multi-projective variety
• point(MultiprojectiveVariety) -- pick a random rational point on a multi-projective variety
• projectionMaps(MultiprojectiveVariety) -- see projectionMaps -- projections of a multi-projective variety
• projections(MultiprojectiveVariety) -- see projections -- projections of a multi-projective variety
• random(List,MultiprojectiveVariety) -- get a random hypersurface of given multi-degree containing a multi-projective variety
• random(ZZ,MultiprojectiveVariety) -- see random(List,MultiprojectiveVariety) -- get a random hypersurface of given multi-degree containing a multi-projective variety
• random(MultiprojectiveVariety) -- apply a random automorphism of the ambient multi-projective space
• RAT MultiprojectiveVariety -- rational map defined by a linear system of hypersurfaces through a variety
• rationalMap(List,MultiprojectiveVariety) -- the multi-rational map defined by a list of rational maps
• rationalMap(MultiprojectiveVariety,Tally) -- rational map defined by an effective divisor
• rationalMap(MultiprojectiveVariety,Tally,List) -- see rationalMap(MultiprojectiveVariety,Tally) -- rational map defined by an effective divisor
• ring(MultiprojectiveVariety) -- the coordinate ring of the variety
• segre(MultiprojectiveVariety) -- the Segre embedding of the variety
• segreEmbedding(MultiprojectiveVariety) -- see segreEmbedding -- the Segre embedding of the variety
• shape(MultiprojectiveVariety) -- shape of the ambient multi-projective space of a multi-projective variety
• rationalMap(MultiprojectiveVariety) -- see shortcuts -- Some convenient shortcuts for multi-rational maps consisting of a single rational map
• rationalMap(MultiprojectiveVariety,List) -- see shortcuts -- Some convenient shortcuts for multi-rational maps consisting of a single rational map
• rationalMap(MultiprojectiveVariety,ZZ) -- see shortcuts -- Some convenient shortcuts for multi-rational maps consisting of a single rational map
• rationalMap(MultiprojectiveVariety,ZZ,ZZ) -- see shortcuts -- Some convenient shortcuts for multi-rational maps consisting of a single rational map
• singularLocus(MultiprojectiveVariety) -- the singular locus of the variety
• support(MultiprojectiveVariety) -- support of a multi-projective variety
• topComponents(MultiprojectiveVariety) -- union of the top dimensional components of a multi-projective variety

For the programmer

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