Projective toric varieties of codimension 2 with maximal Castelnuovo–Mumford regularity

The Eisenbud–Goto conjecture states that reg X ≤ deg − codim + 1 for a nondegenerate irreducible projective variety over an algebraically closed field. While this is known to be false in general, it has been proven several special cases, including when toric of codimension 2. We classify the varieties 2 having maximal regularity, is, which equality holds bound. also give combinatorial characterizations arithmetically Cohen–Macaulay regularity characteristic 0.