Monomial gorenstein curves in A4 as set-theoretic complete intersections

Certain Minimal Varieties Are Set-Theoretic Complete Intersections

“…Big classes of s.t.c.i. ideals generated by binomials have been characterized among the toric ideals (see, e.g., Barile and Lyubeznik, 2005;Barile et al, 2002;Bresinsky, 1979;Eliahou, 1984;Eto, 1994;Katsabekis, 2005;Patil, 1990 for toric curves), and some cases are also known among the determinantal ideals of 2-row matrices. One of these was treated by Robbiano and Valla (1983a), another one by Verdi (1979).…”

Almost complete intersection monomial curves inA4

“…Applying Lemma 2.1 (1) to F-(v4), we may assume -u;(v4) < a; for i = 1,2,3. It may happen new fi, f3, f4 do not satisfy the condition of Lemma 2.1 (2). Then this case is done by Proposition 2.2.…”

The monomial curves associated with balanced semigroups are set-theoretic complete intersections

“…We may assume σ 2 (v 1 )/d 2 σ 3 (v 1 )/d 3 , by interchanging n 2 with n 3 if necessary. By Lemma 5.1 (2),…”