Set-theoretic complete intersections on binomials

Abstract

Let V be an affine toric variety of codimension r over a field of any characteristic. We completely characterize the affine toric varieties that are set-theoretic complete intersections on binomials. In particular we prove that in the characteristic zero case, V is a set-theoretic complete intersection on binomials if and only if V is a complete intersection. Moreover, if F 1 ,..., F r are binomials such that I(V) = rad(F 1 ,...,F r ), then I(V) = (F 1 ,...,F r ). While in the positive characteristic p case, V is a set-theoretic complete intersection on binomials if and only if V is completely p-glued. These results improve and complete all known results on these topics.