SET-THEORETIC COMPLETE INTERSECTIONS ON BINOMIALS, THE SIMPLICIAL TORIC CASE
DOI:
https://doi.org/10.15381/pes.v3i2.9245Abstract
Let V be a simplicial toric variety of codimension r over a field of any characteristic. We completely characterize the implicial toric varieties that are set-theoretic complete intersections on binomials. In particular we prove that:1. In characteristic zero, V is a set-theoretic complete intersection on binomials if and only jf V is a. complete intersection. Moreover, if F1,…,Fr; are binomials such that I(V)= rad( F1, . .. ,Fr), th en I(V) = (F1, ... ,Fr).
We also get a geometric proof of some of the results in [9] characterizing complete intersections by gluing; semigroups.
2. In positive characteristic p, V is a set-theoretic complete intersection on binomials if and only if V is complete 1y p-glued. These results improve and complete all known results on these topics.
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Copyright (c) 2000 Margherita Barile, Marcel Morales, Apostolos Thoma
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