… non reduced schemes. Still, some of them, the so–called ropes are relatively nice (a rope
on a smooth, irreducible projective curve Y of Pr, is locally Cohen–Macaulay and contained in …

… to the Cohen – Macaulay Schemes over the Serre duality on Smooth Schemes for category
… CohenMacaulay can be given over a sub-scheme 𝑆 𝑉 ∀𝑋𝑐 ⊂ ℙ𝑛 then the ideal sheaf …

… Cohen-Macaulay property is formally defined, a review of other equivalent frameworks more
suitable for graphs or arithmetical … For arithmetic problems it is appropriate to work within the …

… ), a vector bundle E on Y is called arithmetically Cohen–Macaulay (aCM) if all its intermediate …
Given a positive integer m, we denote the Quot-scheme parameterizing subscheme Z ⊂ Y …

… The unmixed degree is a natural generalization of the ordinary degree as well as the
arithmetic degree (for the definition of arithmetic degree, adeg(I,M), we refer to Definition 5.1). We …

… To state our main theorem, we recall the notion of arithmetic degree, introduced by Bayer
and Mumford in [3] (see also [21, 22]). First, recall that if \(0\ne M\) is a finitely generated \(\…

… scheme of points in the plane is normal, Cohen–Macaulay and … scheme over the principal
component of Hilbn(Cd) is Cohen–… Let S ⊂ PN be a projective arithmetically Cohen–Macaulay …

… of 0-dimensional schemes, which are always aCM. Nevertheless, the only knowledge of 0-…
schemes is not sufficient to give answers to our question because we deal also with schemes …

… Hilbert schemes Hd , g of locally Cohen–Macaulay curves C⊂ P3 of degree d and arithmetic
… connectedness of the Hilbert scheme Hd , g of locally Cohen– Macaulay curves in P3= P3 …

… modules which obstruct the Cohen-Macaulay property. Work ofBrodmann [Br2] … arithmetic
Macaulayfication for local rings whose completions areequidimensional and Cohen-Macaulay …