2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132497We 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 RossiCommutative AlgebraAlgebraic Geometry14M10; 14M25; 14F20text