EmbeddedProjectiveVariety -- the class of all embedded projective varieties

i1 : X = PP_QQ^(2,2);

o1 : ProjectiveVariety, surface in PP^5

i2 : class X

o2 = EmbeddedProjectiveVariety

o2 : Type

i3 : Y = X ** X;

o3 : ProjectiveVariety, X x X

i4 : class Y

o4 = MultiprojectiveVariety

o4 : Type

Types of embedded projective variety :

• GrassmannianVariety -- the class of all Grassmannians of linear subspaces of projective spaces

Functions and methods returning an embedded projective variety :

• coneOfLines -- cone of lines on a subvariety passing through a point

Methods that use an embedded projective variety :

• chowForm(EmbeddedProjectiveVariety) -- chow forms of a projective variety
• "coneOfLines(EmbeddedProjectiveVariety,EmbeddedProjectiveVariety)" -- see coneOfLines -- cone of lines on a subvariety passing through a point
• conormalVariety(EmbeddedProjectiveVariety) -- the conormal variety of a projective variety
• "cycleClass(EmbeddedProjectiveVariety)" -- see cycleClass -- determine the expression of the class of a cycle as a linear combination of Schubert classes
• dual(EmbeddedProjectiveVariety) -- the variety projectively dual to an embedded projective variety
• EmbeddedProjectiveVariety ! -- print a more detailed description of an embedded projective variety
• EmbeddedProjectiveVariety ++ EmbeddedProjectiveVariety -- join of projective varieties
• "EmbeddedProjectiveVariety <=== EmbeddedProjectiveVariety" -- see EmbeddedProjectiveVariety ===> EmbeddedProjectiveVariety -- try to find an isomorphism between two projective varieties
• EmbeddedProjectiveVariety ===> EmbeddedProjectiveVariety -- try to find an isomorphism between two projective varieties
• "Fano(EmbeddedProjectiveVariety)" -- see Fano(ZZ,EmbeddedProjectiveVariety) -- Fano scheme of a projective variety
• Fano(ZZ,EmbeddedProjectiveVariety) -- Fano scheme of a projective variety
• "GG(EmbeddedProjectiveVariety)" -- see GG -- the Grassmannian of k-dimensional linear subspaces of an n-dimensional projective space
• "GG(ZZ,EmbeddedProjectiveVariety)" -- see GG -- the Grassmannian of k-dimensional linear subspaces of an n-dimensional projective space
• "linearlyNormalEmbedding(EmbeddedProjectiveVariety)" -- see linearlyNormalEmbedding -- get the linearly normal embedding
• "linearSpan(EmbeddedProjectiveVariety)" -- see linearSpan -- the linear span of an embedded projective variety
• "RationalMap ^** EmbeddedProjectiveVariety" -- see MultirationalMap ^** MultiprojectiveVariety -- inverse image via a multi-rational map
• "sectionalGenus(EmbeddedProjectiveVariety)" -- see sectionalGenus -- the sectional genus of an embedded projective variety
• tangentCone(EmbeddedProjectiveVariety,EmbeddedProjectiveVariety) -- tangent cone to a projective variety at a point
• tangentialChowForm(EmbeddedProjectiveVariety,ZZ) -- higher Chow forms of a projective variety
• "tangentSpace(EmbeddedProjectiveVariety,EmbeddedProjectiveVariety)" -- see tangentSpace -- tangent space to a projective variety at a point
• variety(EmbeddedProjectiveVariety) -- convert an embedded projective variety into a built-in projective variety

For the programmer

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