On simplicial toric varieties of codimension 2

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We describe classes of toric varieties of codimension 2 which are either minimally defined by 3 binomial equations over any algebraically closed field, or are set-theoretic complete intersections in exactly one positive characteristic.
Revised version. To appear in: Rendiconti dell'Istituto di Matematica dell'Universita' di Trieste. Dedicated to the memory of Fabio Rossi

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