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Non-Cohen-Macaulay Symbolic Blow-ups for Space Monomial Curves
| Content Provider | Scilit |
|---|---|
| Author | Morimoto, Mayumi Goto, Shiro |
| Copyright Year | 1992 |
| Description | Let $\mathfrak {p} = \mathfrak {p}({n_1},{n_2},{n_3})$ denote the prime ideal in the formal power series ring $A = k[[X,Y,Z]]$ over a field $k$ defining the space monomial curve $X = {T^{{n_1}}},Y = {T^{{n_2}}}$, and $Z = {T^{{n_3}}}$ with $\operatorname {GCD} ({n_1},{n_2},{n_3}) = 1$. Then the symbolic Rees algebra ${R_s}(\mathfrak {p}) = { \oplus _{n \geq 0}}{\mathfrak {p}^{(n)}}$ for $\mathfrak {p} = \mathfrak {p}({n^2} + 2n + 2,{n^2} + 2n + 1,{n^2} + n + 1)$ is Noetherian but not Cohen-Macaulay if ${\text {ch}}k = p > 0$ and $n = {p^e}$ with $e \geq 1$. The same is true for $\mathfrak {p} = \mathfrak {p}({n^2},{n^2} + 1,{n^2} + n + 1)$ if ${\text {ch}}k = p > 0$ and $n = {p^e} \geq 3$ . |
| Related Links | https://www.ams.org/proc/1992-116-02/S0002-9939-1992-1095226-6/S0002-9939-1992-1095226-6.pdf |
| Ending Page | 311 |
| Page Count | 7 |
| Starting Page | 305 |
| ISSN | 00029939 |
| e-ISSN | 10886826 |
| DOI | 10.2307/2159734 |
| Journal | Proceedings of the American Mathematical Society |
| Issue Number | 2 |
| Volume Number | 116 |
| Language | English |
| Publisher | Duke University Press |
| Publisher Date | 1992-10-01 |
| Access Restriction | Open |
| Subject Keyword | Logic Cohen Macaulay Symbolic Space Monomial Monomial Curves Mathfrak N_2 |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
