The main result of this paper is a numerical criterion to characterize free complete intersection affine simplicial toric varieties. Free complete intersection affine simplicial semigroups were introduced and studied by J. C. Rosales and P. A. García-Sánchez [Semigroup Forum 58 (1999), no. 3, 367–385]. An affine simplicial toric variety is said to be a free complete intersection if its corresponding semigroup is so. Such a variety is, in particular, a complete intersection. The numerical criterion obtained in this paper is in terms of the solvability of some linear congruences for the exponents of the parametrization of the variety. As an application, the particular case of codimension 2 is studied in detail.
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