Timeline for the generators of $I$ when $\mathbb C[x,y]/I$ is Gorenstein with zero dimension
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 10, 2012 at 18:19 | answer | added | Youngsu | timeline score: 0 | |
| Aug 10, 2012 at 13:40 | answer | added | Mohan | timeline score: 4 | |
| Aug 10, 2012 at 12:45 | comment | added | Pham Hung Quy | Could you give the reference for the claim: If $R$ is local then $I$ generated by a regular sequence? | |
| Aug 10, 2012 at 7:49 | comment | added | J.C. Ottem | What do you mean by '$R$ is already local'? | |
| Aug 10, 2012 at 3:52 | comment | added | David White | It's pretty late here, so I hope this isn't completely nonsensical. A Gorenstein ring is Cohen-Macaulay and both $R_m$ and $R$ are local Gorenstein and so local Cohen-Macaulay. For such rings any ideal $I$ has height equal to the depth of $I$ with respect to $I$. See e.g. en.wikipedia.org/wiki/Height_(ring_theory). Also, all regular sequences in $I$ have length equal to the depth of $I$, see en.wikipedia.org/wiki/Depth_(algebra). Now, $R$ is already local, so it seems height = depth = length of longest regular sequence even without this bit about $R_m$. How does that sound? | |
| Aug 10, 2012 at 2:59 | history | asked | Xingting | CC BY-SA 3.0 |