Cohen-Macaulay and Gorenstein property of Rees algebras of non-singular equimultiple prime ideals
The main purpose of this paper is to study the problem when the Rees algebra \(R({\mathfrak p})\) of a height 2 non-singular equimultiple prime ideal \({\mathfrak p}\) of some local ring \(A\) is a Cohen-Macaulay, respectively Gorenstein ring. The paper deals with the conjecture, which asserts that the Gorenstein property of \(R({\mathfrak p})\) implies that of \(A\) when \(\dim A=3\), the case \(\dim A\geq 4\) having been settled positively by Herrmann and Ikeda. Note that the analogous question for the Cohen-Macaulay property has been proven to have a negative answer by Hermann, Ribbe and the first named author. Here it is shown (besides a thorough study of the CM and Gorenstein problem in arbitrary characteristic) that the conjecture has a positive answer if \(\text{char }K\neq 2\) and if \(v(p)\leq 3\), where \(v(p)\) is the minimal number of generators of \(p\), whereas counterexamples may be given otherwise.
scientific article; zbMATH DE number 97888
scientific article