Timeline for Is a smooth intersection of hypersurfaces equidimensional?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Aug 2, 2018 at 14:58 | history | edited | Roberto Pagaria | CC BY-SA 4.0 |
added a more precise and general statement.
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| Jul 28, 2018 at 22:27 | comment | added | R. van Dobben de Bruyn | If $V_i$ are allowed to be effective divisors (as opposed to ample divisors; cf. the comments below Sándor Kovács's answer), it seems likely that the following can happen: $V_1$, $V_2$, and $V_3$ are smooth irreducible divisors, $V_{12}$, $V_{23}$, and $V_{31}$ each consist of two smooth components, one of which is in common between all three, and the others intersect in a lower-dimensional variety. Then $V_{123}$ has components of different dimensions. I've tried to construct such an example, but so far have been unsuccessful. | |
| Jul 27, 2018 at 20:17 | answer | added | Sándor Kovács | timeline score: 5 | |
| Jul 27, 2018 at 15:26 | history | asked | Roberto Pagaria | CC BY-SA 4.0 |