Toward parametric Cohen-Macaulayfication of two-dimensional finite local cohomology domains
We show that if (R,\({\mathfrak M})\) is a 2-dimensional local domain having finite local cohomology module \(H^ 1_{{\mathfrak M}}(R)\) (equivalently, R is a 2-dimensional local unmixed domain), and having algebraically closed residue field, such that \({\mathfrak M}^ 2\) is included in \(Ann(H^ 1_{{\mathfrak M}}(R))\), then any sequence of \(\ell +2\) successive parametric blowings-up of R necessarily produces a Cohen-Macaulay scheme, where \(\ell:=[\frac{\ell_ R(H^ 1_{{\mathfrak M}}(R))}{2}]\) (greatest integer). This gives a measure of the ``non-Cohen-Macaulayness'' of the singularity, partially generalizing results of Goto, Schenzel, et al. Some related ideal-theoretic results and some examples are included.
scientific article; zbMATH DE number 4175114