Timeline for When a sum of the ideals is radical
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Feb 2, 2023 at 19:11 | vote | accept | Adam | ||
| Feb 1, 2023 at 14:42 | answer | added | Zach Teitler | timeline score: 2 | |
| Jan 31, 2023 at 18:23 | comment | added | Zach Teitler | (I can write that in an answer, but surely it's got a citeable reference in some book..? Does anyone know where it might be found?) | |
| Jan 31, 2023 at 5:33 | history | edited | Adam | CC BY-SA 4.0 |
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| Jan 31, 2023 at 5:19 | comment | added | Zach Teitler | Let $Z$ be an irreducible component of $X \cap Y$ and $p \in Z$. Say $\dim X = a$, $\dim Y = b$. By smoothness, $\dim T_p X = a$ and $\dim T_p Y = b$ as well. By transversality, $\dim T_p X \cap T_p Y = a+b-n$. On one hand, $T_p Z \subseteq T_p X \cap T_p Y$. So $\dim T_p Z \leq a+b-n$. On other hand, $\dim Z \geq a+b-n$ (math.stackexchange.com/questions/3418995/…). So $\dim T_p Z = \dim Z$. – Relaxing smoothness seems doubtful: the very simplest possible example is a counterexample as you described. | |
| Jan 31, 2023 at 3:22 | comment | added | Adam | @StevenLandsburg Thanks, fixed now. | |
| Jan 31, 2023 at 3:22 | history | edited | Adam | CC BY-SA 4.0 |
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| Jan 31, 2023 at 3:09 | comment | added | Steven Landsburg | Presumably you mean $T_pX+T_pY$, not $T_pX\cup T_pY$, yes? | |
| Jan 31, 2023 at 3:00 | history | edited | Adam | CC BY-SA 4.0 |
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| Jan 30, 2023 at 23:50 | history | asked | Adam | CC BY-SA 4.0 |