Set-theoretic complete intersections on binomials
Margherita Barile, Marcel Moralès, Apostolos Thoma · Proceedings of the American Mathematical Society · 2001
Let V V be an affine toric variety of codimension r 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 V is a set-theoretic complete intersection on binomials if and only if V V is a complete intersection. Moreover, if F 1 , … , F r F_1,\dots ,F_r are binomials such that I ( V ) = r a d ( F 1 , … , F r ) I(V) = rad(F_1,\dots , F_r) , then I ( V ) = ( F 1 , … , F r ) I(V) = (F_1,\dots ,F_r) . While in the positive characteristic p p case, V V is a set-theoretic complete intersection on binomials if and only if V V is completely p p -glued. These results improve and complete all known results on these topics.