Timeline for How to check if a commutative ring is Gorenstein.
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Feb 18, 2013 at 22:28 | comment | added | Graham Leuschke | Dear Sándor, of course I was not offended. You're right -- our answers complement each other. In fact, a full list of all the ways to answer this question might involve a pretty broad cross-section of commutative algebra and algebraic geometry. | |
| Feb 18, 2013 at 15:29 | comment | added | Sándor Kovács | ps: I am also glad your solution is here, because the two sides together give a much more complete picture than either one would in themselves. | |
| Feb 18, 2013 at 15:28 | comment | added | Sándor Kovács | Dear Graham, I did not mean the first line of my answer be a criticism of your answer. In fact, I am sure that for the OP this is much closer to what they wanted. My point was that while I have high appreciation for the usefulness of Macaulay 2 or computational tools in general, it is sometimes useful to recognize the situation at hand. For me, it would have been difficult to figure out what you did, but when I looked at the equations I thought of rank $1$ matrices and once I saw the geometry I knew what was happening. I thought it was worth sharing. | |
| Feb 18, 2013 at 12:16 | comment | added | Graham Leuschke | Yes, absolutely. | |
| Feb 18, 2013 at 5:17 | comment | added | Youngsu | Hi. Another sleek way could be using resolution of $I$. Since $I$ is homogeneous, I believe Macaulay2 computes minimal graded free resolution for $I$. i20 : res I 1 3 2 o20 = S <-- S <-- S <-- 0 0 1 2 3 1) This shows that $I$ is Cohen-Macaulay (by Hilbert-Burch), but not Gorenstein by the same argument on Socle. 2) Since ideal $I$ is of codimension $2$, it is locally Gorenstein if and only if it is complete intersection. However the first Betti number shows that it is minimally three generated. | |
| Feb 18, 2013 at 2:46 | vote | accept | Qlzqlzuup | ||
| Feb 18, 2013 at 2:41 | vote | accept | Qlzqlzuup | ||
| Feb 18, 2013 at 2:46 | |||||
| Feb 18, 2013 at 2:28 | history | edited | Graham Leuschke | CC BY-SA 3.0 |
added alt. method
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| Feb 18, 2013 at 1:45 | history | edited | Graham Leuschke | CC BY-SA 3.0 |
added 49 characters in body
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| Feb 18, 2013 at 1:22 | history | answered | Graham Leuschke | CC BY-SA 3.0 |