chap3.txt

  
  3 Affine toric varieties
  
  This chapter concerns toric commands which deal with the coordinate rings of
  affine toric varieties U_σ.
  
  
  3.1 Ideals defining affine toric varieties
  
  3.1-1 EmbeddingAffineToricVariety
  
  EmbeddingAffineToricVariety( L )  function
  
  Input: L is a list generating a cone (as in DualSemigroupGenerators).
  Output:  the  toroidal  embedding  of X=Spec(I), where I is the ideal of the
  affine toric variety (given as a list of multinomials).
  
    Example  
    gap> phi:=EmbeddingAffineToricVariety([[1,0],[3,4]]);
    [ x_2, x_1, x_1^2/x_4, x_1^3/x_4^2, x_1^4/x_4^3 ]
    gap> L:=[[1,0,0],[1,1,0],[1,1,1],[1,0,1]];;
    gap> phi:=EmbeddingAffineToricVariety(L);
    [ x_3, x_2, x_1/x_5, x_1/x_6 ]