GAP (toric) - Chapter 3: Affine toric varieties

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3 Affine toric varieties
3.1 Ideals defining affine toric varieties
3.1-1 EmbeddingAffineToricVariety

### 3 Affine toric varieties

This chapter concerns toric commands which deal with the coordinate rings of affine toric varieties \(U_\sigma\).

#### 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).

    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 ]

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