In this paper, we study the problem of determining set-theoretic and ideal-theoretic complete intersection monomial curves in affine and projective n-space. Starting with a monomial curve which is a set-theoretic (resp. ideal-theoretic) complete intersection in (n − 1)-space we produce infinitely many new examples of monomial curves that are set-theoretic (resp. idealtheoretic) complete interse...

In this paper we produce infinitely many examples of set-theoretic complete intersection monomial curves in P n+1 , starting with a set-theoretic complete intersection monomial curve in P n. In most of the cases our results cannot be obtained through semigroup gluing technique and we can tell apart explicitly which cases are new.

Let ∆ be a simplicial complex and χ be an s-coloring of ∆. Biermann and Van Tuyl have introduced the simplicial complex ∆χ. As a corollary of Theorems 5 and 7 in their 2013 article, we obtain that the Stanley–Reisner ring of ∆χ over a field is Cohen–Macaulay. In this note, we generalize this corollary by proving that the Stanley–Reisner ideal of ∆χ over a field is set-theoretic complete interse...

This is an expository account based mainly on an article by Jack Ohm titled “Space curves as ideal-theoretic intersections”. It also gives a proof of the fact that smooth space curves can be realized as set-theoretic complete intersections. The penultimate section proves the theorem of Cowsik and Nori : Curves in affine n-space of characteristic p are set-theoretic complete intersection.

Let A be a regular ring of dimension d ( d ≥ 3 ) containing an infinite field k. Let n be an integer such that 2n ≥ d+3. Let I be an ideal in A of height n and P be a projective Amodule of rank n. Suppose P ⊕A ≈ A and there is a surjection α: P → I. It is proved in this note that I is a set theoretic complete intersection ideal. As a consequence, a smooth curve in a smooth affine C-algebra with...