Almost complete intersection monomial curves inA⁴

On toric varieties which are almost set-theoretic complete intersections

“…, n − 1. Hence, by (11), v = u, which completes the proof that φ is injective. Since it is finite, it is proper.…”

Set-theoretic complete intersection lattice ideals in monoid rings

“…If N = 4 and if I (V ) is an almost complete intersection, we can apply Theorem 3.1 and show that it is a set-theoretic complete intersection [8]. We will give another example of set-theoretic complete intersection monomial curve initially proved in [18].…”

“…In this case, if the defining ideal of C is generated by N − 1 binomials up to radical, then it turns out to be a complete intersection [20]. There are number of results in which the monomial curves are set-theoretic complete intersections [2,4,5,7,8,12,13,18,19,21], but almost all of them find N − 2 binomials and one polynomial which define the monomial curves set-theoretically. So, in this article, we ask under what conditions there are N − 2 binomials and one polynomial which define a monomial curve set-theoretically.…”

“…Example 3.3 [5,8,14]. If N = 3, and if I (V ) is not a complete intersection, then it is an almost complete intersection and there are…”

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

“…If (X 1 , X 2 , X 3 ) is a lattice divisor of I (W 3 ), then, by Lemma 3 ) is a set-theoretic complete intersection, hence so is I (V ). (Step 2) Assume that I (V ) is an almost complete intersection.…”