The Gorensteinness of the symbolic blow-ups for certain space monomial curves
The Gorensteinness of the symbolic blow-ups for certain space monomial curves
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某些空间单项曲线的符号放大的 Gorensteinness
DOI：
10.1090/s0002-9947-1993-1124166-4
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
Y. Shimoda
中科院分区：
文献类型：
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作者：
S. Goto;Koji Nishida;Y. Shimoda
设p = p（n1，n2，n3）表示域k上的形式幂级数环A = k[[X，Y，Z]]中的素理想，该环定义了空间单项曲线X = Tn 1，Y = Tn 2，Z = Tn 3，且GCD（n1，n2，n3）= 1.则符号Rees代数Rs（p）= ○+ n ≥ 0 p（n）是Gorenstein环，其中p = p（n1，n2，n3）的素理想min{n1，n2，n3} = 4，p = p（m，m + 1，m + 4）的素理想m = 9，13.当chk = 3时，p = p（9，10，13）和p = p（13，14，17）的环Rs（p）是Noether环，但不是Cohen-Macaulay环
Let p = p(n 1 , n 2 , n 3 ) denote the prime ideal in the formal power series ring A = k[[X, Y, Z]] over a field k defining the space monomial curve X = T n1 , Y = T n2 , and Z = T n3 with GCD(n 1 , n 2 , n 3 ) = 1. Then the symbolic Rees algebras R s (p) = ○+ n ≥ 0 p (n) are Gorenstein rings for the prime ideals p = p(n 1 , n 2 , n 3 ) with min{n 1 , n 2 , n 3 } = 4 and p = p(m, m + 1, m + 4) with m ¬= 9, 13. The rings R s (p) for p = p(9, 10, 13) and p = p(13, 14, 17) are Noetherian but non-Cohen-Macaulay, if ch k = 3