Complete intersections in simplicial toric varieties ?
Given a set A={a1,,an}?Nm A = { a 1 ,  , a n } ? N m of nonzero vectors defining a simplicial toric ideal IA?k[x1,,xn] I A ? k [ x 1 ,  , x n ] , where k  is an arbitrary field, we provide an algorithm for checking whether IA I A is a complete intersection. This algorithm does not require the explicit computation of a minimal set of generators of IA I A . The algorithm is based on the application of some new results concerning toric ideals to the simplicial case. For homogeneous simplicial toric ideals, we provide a simpler version of this algorithm. Moreover, when k is an algebraically closed field, we list all ideal-theoretic complete intersection simplicial projective toric varieties that are either smooth or have one singular point.
complete intersection simplicial toric ideal algorithm singularities