# EmbeddedProjectiveVariety -- the class of all embedded projective varieties

## Description

The embedded projective varieties are exactly the multi-projective varieties embedded in a single projective space; so that $X$ is an embedded projective variety if and only if # shape X == 1.

 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

## For the programmer

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