On Cohen-Macaulayness and Gorensteinness of Rees algebras of integrally closed filtrations of height two equimultiple ideals
Let \((A,m)\) be a local ring with \(\dim A= d>0\) and \(I\) be an ideal of \(A\) with \(\text{ht} (I)> 0\). The integral closure of \(I\) is denoted by \(\overline{I}\) and the graded ring \(R(I)= \bigoplus \overline{I^n} t^n\) is defined as the normalized Rees algebra of \(I\). In this paper under review the author studies the Cohen-Macaulay and Gorenstein properties of the normalized Rees algebra of height two ideals. For Cohen-Macaulay rings \(A\), the problem was investigated in a series of papers by Goto, Nishida, Hoa, Zarzuela and Itoh.
scientific article; zbMATH DE number 1268014