Timeline for Is being reduced a generic property of schemes?
Current License: CC BY-SA 4.0
16 events
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| Feb 7, 2023 at 1:27 | comment | added | Utf | Dear @SándorKovács, thanks a lot for the clarification. I had just posted a somehow similar question, when I read your comment and thought that my question could maybe be already answered by that...but unfortunately that's just not the case, apparently. | |
| Feb 6, 2023 at 20:33 | comment | added | Sándor Kovács | Dear @Utf, the point of this answer was to give an example that the assumption in #3 in the original question was still not enough for the desired conclusion. In other words, the $Y$ here is supposed to be a complete intersection in $X$. I added a clarification to that end. I hope it makes more sense now. | |
| Feb 6, 2023 at 20:29 | history | edited | Sándor Kovács | CC BY-SA 4.0 |
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| Feb 6, 2023 at 13:04 | comment | added | Utf | @SándorKovács I'm sorry for reopening this post after so much time, but I am confused about something you said: if I understood correctly you claimed that if $Y$ is a subvariety of $X$, and $X$ is at least $S_{t+1}$ with $t=codim_XY$, then $Y$ is $S_1$. But let's take $X=\mathbb A^2$ and $Y=V(x^2, xy)$, i.e. the vertical line with a double origin: $X$ should be $S_k$ for any $k$ (since it's Cohen–Macaulay), but $Y$ is not $S_1$, since it has an embedded prime...where am I wrong? | |
| Jan 21, 2015 at 7:24 | history | edited | Sándor Kovács | CC BY-SA 3.0 |
typos
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| Jan 20, 2015 at 14:04 | vote | accept | pinaki | ||
| Jan 20, 2015 at 6:55 | history | edited | Sándor Kovács | CC BY-SA 3.0 |
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| Jan 20, 2015 at 6:47 | history | edited | Sándor Kovács | CC BY-SA 3.0 |
typo
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| Jan 20, 2015 at 2:38 | history | edited | Sándor Kovács | CC BY-SA 3.0 |
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| Jan 20, 2015 at 2:34 | comment | added | Sándor Kovács | You're right. My original answer was different, then I forgot half of the assumptions and made an edit (actually several) and ended up with this. I have a new example which looks much better now. Cheers! | |
| Jan 20, 2015 at 2:32 | history | edited | Sándor Kovács | CC BY-SA 3.0 |
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| Jan 20, 2015 at 2:14 | history | edited | Sándor Kovács | CC BY-SA 3.0 |
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| Jan 19, 2015 at 23:40 | comment | added | pinaki | Dear Sándor, not sure I get the example: your $Y$ is nowhere reduced, so it does not satisfy the assumption of being generically reduced. | |
| Jan 19, 2015 at 22:50 | history | edited | Sándor Kovács | CC BY-SA 3.0 |
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| Jan 19, 2015 at 22:40 | history | edited | Sándor Kovács | CC BY-SA 3.0 |
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| Jan 19, 2015 at 22:26 | history | answered | Sándor Kovács | CC BY-SA 3.0 |