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, ..., Fr are binomials such that I(V) = rad(F1, ... , Fr), then I(V) = (F1, ... , Fr). 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.
Set-theoretic complete intersections on binomials
BARILE, Margherita;
2002-01-01
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 F1, ..., Fr are binomials such that I(V) = rad(F1, ... , Fr), then I(V) = (F1, ... , Fr). 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
