Timeline for What is the most simple non-planar Gorenstein curve singularity?
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| Oct 6, 2012 at 15:22 | answer | added | jlk | timeline score: 3 | |
| Jun 1, 2010 at 2:41 | history | edited | jlk | CC BY-SA 2.5 |
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| May 31, 2010 at 4:11 | comment | added | jlk | @Hailong Dao: I agree. Its a bit harder to see this than for the other example, though. | |
| May 31, 2010 at 2:31 | history | edited | jlk | CC BY-SA 2.5 |
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| May 31, 2010 at 2:12 | vote | accept | jlk | ||
| May 30, 2010 at 4:59 | answer | added | Hailong Dao | timeline score: 6 | |
| May 30, 2010 at 3:15 | comment | added | Hailong Dao | @jlk: I think your example is also an intersection of 4 lines : $(y,z)$ and $y-az, x-a^2z$ with $a^3=1$. | |
| May 30, 2010 at 2:30 | history | edited | jlk | CC BY-SA 2.5 |
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| May 28, 2010 at 21:35 | comment | added | jlk | (continued): If you are curious, I can try to reconstruct the details. The example of 4-lines in 3-space shows that $\delta=4$ can be achieved by a non-planar Gorenstein curve singularity, and this is maybe a nicer examples than $k[[xyz]](xy−z^2, zx=y^22)$. | |
| May 28, 2010 at 20:48 | comment | added | jlk | @Hailong Dao: I computed delta directly from the definitions. The computation is similar to, but harder than, the example of 4 lines in 3-space given in response to Graham's question. Unless I made a mistake, I think the normalization $\tilde{R}$ is isomorphic to the product of 4 power series rings. As a complete $k$-algebra contained in $\tilde{R}$, $R$ is generated by 3 4-tuples of degree 1 monomials. The quotient \tilde{R}/R has basis given by (1,0,0,0), (0,1,0,0), (0,0,1,), and a 4-tuple in which the entries are degree 1 monomials. | |
| May 28, 2010 at 4:02 | comment | added | Hailong Dao | @jlk: why does delta=4 in your example? | |
| May 27, 2010 at 16:52 | history | edited | jlk | CC BY-SA 2.5 |
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| May 27, 2010 at 15:29 | history | edited | jlk | CC BY-SA 2.5 |
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| May 27, 2010 at 15:13 | history | edited | jlk | CC BY-SA 2.5 |
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| May 26, 2010 at 19:42 | comment | added | David E Speyer | Comments about confusion about $\delta$ deleted. | |
| May 26, 2010 at 19:34 | answer | added | Graham Leuschke | timeline score: 5 | |
| May 26, 2010 at 18:59 | history | edited | jlk | CC BY-SA 2.5 |
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| May 26, 2010 at 18:30 | history | edited | jlk | CC BY-SA 2.5 |
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| May 26, 2010 at 6:12 | history | edited | jlk | CC BY-SA 2.5 |
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| May 26, 2010 at 4:56 | history | asked | jlk | CC BY-SA 2.5 |