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D.15.35.3 productVariety

Procedure from library schubert.lib (see schubert_lib).

Usage:
productVariety(U,V); U variety, V variety

Input:
two abstract varieties

Output:
a product variety as an abstract variety

Return:
variety

Example:
 
LIB "schubert.lib";
variety P = projectiveSpace(3);
variety G = Grassmannian(2,4);
variety W = productVariety(P,G);
W;
==> A variety of dimension 7
==> 
W.dimension == P.dimension + G.dimension;
==> 1
def r = W.baseRing;
setring r;
W.relations;
==> _[1]=h^4
==> _[2]=q(1)^3-2*q(1)*q(2)
==> _[3]=q(1)^4-3*q(1)^2*q(2)+q(2)^2
See also: Grassmannian; projectiveBundle; projectiveSpace.