摘要
In a Cohen-Macaulay local ring(A,m),we study the Hilbert function of an integrally closed m-primary ideal I whose reduction number is three.,With a mild assump-tion we give an inequality ιA(A/I)≥e0(I)-e1(I)+(e2(I)+lA(I^(2)/QI)/2,where ei(I)denotes the ith Hilbert coeficient and Q denotes a minimal reduction of I.The inequality is located between inequalities of Itoh and Elias-Valla.Furthermore,this inequality be-comes an equality if and only if the depth of the associated graded ring of I is larger than or equal to dim A-1.We also study the Cohen-Macaulayness of the associated graded rings of determinantal rings.
基金
Supported by JSPS KAKENHI Grant Number JP19J10579 and JP21K13766。
