LAUSR

A new transparent proof of the well-known good compactification theorem for the complex torus $$({\mathbb {C}}^*)^n$$ ( C ∗ ) n is presented. This theorem provides a powerful tool in enumerative geometry for subvarieties in the complex torus. The paper also contains an algorithm constructing a good compactification for a subvariety in $$({\mathbb {C}}^*)^n$$ ( C ∗ ) n explicitly defined by a system of equations. A new theorem on a toroidal-like compactification is stated. A transparent proof of this generalization of the good compactification theorem which is similar to proofs and constructions from this paper will be presented in a forthcoming publication.