On binomial set-theoretic complete intersections in characteristic \(p\) (Q928363)

The article under review deals with a question posed by \textit{M. Barile} and \textit{G. Lyubeznik} [Proc. Am. Math. Soc. 133, No. 11, 3199--3209 (2005; Zbl 1077.14064)], namely whether there could be toric varieties which are set-theoretic complete intersections in a more than one, but not in all positive characteristics. The author provides a negative answer to this question if the toric variety is simplicial and of codimension 2. More precisely she proves that for a simplicial toric variety of codimension 2 the property of being a set-theoretic complete intersection on binomials in characteristic \(p\) holds either for all primes \(p\), or for no prime \(p\), or for exactly one prime \(p\).