Margherita Barile, Marcel Morales, Apostolos Thoma

Set-theoretic complete intersections on binomials

Proc. Amer. Math. Soc. 130 (2002), 1893-1903.

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 F₁, … , F_r are binomials such that I(V) = rad (F₁, … , F_r), then I(V) = (F₁, … , 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.