This paper presents a generalization to the higher-dimensional situation of the main results of the first author about the normality of one-fibered monomial ideals [2, Theoremes 2.4 and 3.8]. Precisely, we show that i...This paper presents a generalization to the higher-dimensional situation of the main results of the first author about the normality of one-fibered monomial ideals [2, Theoremes 2.4 and 3.8]. Precisely, we show that if I is a monomial ideal of R = k[x1, x2,..., Xd], then I is normal one-fibered if and only if for all positive integers n and all x, y in R such that xy ∈ I2n, either x or y belongs to In.展开更多
Let f0, f1, f2, f3 be linearly independent homogeneous quadratic forms in the standard Z-graded ring R ：= K[s, t, u], and gcd（f0, f1, f2, f3） = 1. This defines a rational map Ф ： P2 → P3. The Rees algebra Rees（...Let f0, f1, f2, f3 be linearly independent homogeneous quadratic forms in the standard Z-graded ring R ：= K[s, t, u], and gcd（f0, f1, f2, f3） = 1. This defines a rational map Ф ： P2 → P3. The Rees algebra Rees（I） = R I I2 … of the ideal I = （f0, fl, f2, fs） is the graded R-algebra which can be described as the image of an R-algebra homomorphism h ： R[x, y, z, w] → Rees（I）. This paper discusses the free resolutions of I, and the structure of ker（h）.展开更多
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)+l...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.展开更多
文摘This paper presents a generalization to the higher-dimensional situation of the main results of the first author about the normality of one-fibered monomial ideals [2, Theoremes 2.4 and 3.8]. Precisely, we show that if I is a monomial ideal of R = k[x1, x2,..., Xd], then I is normal one-fibered if and only if for all positive integers n and all x, y in R such that xy ∈ I2n, either x or y belongs to In.
文摘Let f0, f1, f2, f3 be linearly independent homogeneous quadratic forms in the standard Z-graded ring R ：= K[s, t, u], and gcd（f0, f1, f2, f3） = 1. This defines a rational map Ф ： P2 → P3. The Rees algebra Rees（I） = R I I2 … of the ideal I = （f0, fl, f2, fs） is the graded R-algebra which can be described as the image of an R-algebra homomorphism h ： R[x, y, z, w] → Rees（I）. This paper discusses the free resolutions of I, and the structure of ker（h）.
基金Supported by JSPS KAKENHI Grant Number JP19J10579 and JP21K13766。
文摘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.
