For the family of graded lattice ideals of dimension 1, we establish a complete intersection criterion in algebraic and geometric terms. In positive characteristic, it is shown that all ideals of this family are binomial set-theoretic complete intersections. In characteristic zero, we show that an arbitrary lattice ideal which is a binomial set-theoretic complete intersection is a complete intersection.
['Hiram H. López', 'Rafael H. Villarreal']
COMPLETE INTERSECTIONS IN BINOMIAL AND LATTICE IDEALS