Timeline for Krull dimensions and regular sequences
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 4, 2018 at 8:47 | comment | added | BrianT | Thanks. Is there a kind of geometric interpretation of being Macaulay ? In terms of the zero set of $J$ for instance ? | |
| Oct 4, 2018 at 8:34 | comment | added | abx | It needs dimension $n-k$ and CM, as shown by my counter-example. | |
| Oct 4, 2018 at 8:23 | comment | added | BrianT | Sorry to insist, but I don't understand what conditions are sufficient and necessary. Is it enough that $\mathbb{C}[u] / J$ has dimension $n-k$, or does it need to have dimension $n-k$ and be CM, given the two points above ? | |
| Oct 4, 2018 at 3:47 | comment | added | abx | Yes, sorry I didn't make that explicit. | |
| Oct 3, 2018 at 21:26 | comment | added | BrianT | Suppose that it is indeed Cohen-Macaulay. Don’t we need the dimension to be equal (and not at least) $n-k$ ? | |
| Oct 3, 2018 at 16:39 | comment | added | abx | I think that $\mathbb{C}[u]/J$ Cohen-Macaulay is sufficient. | |
| Oct 3, 2018 at 16:07 | comment | added | BrianT | Thank you for your comment. What would be a sufficient additional condition then ? | |
| Oct 3, 2018 at 14:48 | comment | added | abx | No. Take $n=2$, $k=1$, $J=(u_1^2,u_1u_2)$, $I=(u_2)$. Then 1. and 2. are satisfied, but $u_2$ is a zero divisor in $\mathbb{C}[u]/J$. | |
| Oct 3, 2018 at 14:00 | history | asked | BrianT | CC BY-SA 4.0 |