Timeline for Does there exist a relative compactification with flat boundary?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 4, 2014 at 20:45 | comment | added | Cantlog | It would suffice to contract vertical divisors (in the boundary), but I think this is impossible in general in higher dimension. | |
| Mar 4, 2014 at 2:18 | comment | added | Piotr Achinger | Thank you for the useful reference! Do you believe this should be true for $S$ henselian and $X$ of higher dimension? | |
| Mar 2, 2014 at 17:26 | comment | added | Cantlog | There is an example in the book "Néron models", §6.7, Lemma 6 (remove the non-contractibe irreducible component in the closed fiber and let $X$ be an affine open subscheme with non empty closed fiber). The DVR is not henselian. On the other hand, if S is henselian, and $X$ is normal of relative dimension $1$, then the answer to your question is yes by contracting superfluous irreducible components (i.e. those of positive dimension) in the boundary, see op. cit. | |
| Mar 2, 2014 at 5:31 | vote | accept | Piotr Achinger | ||
| Mar 2, 2014 at 4:50 | history | edited | Piotr Achinger | CC BY-SA 3.0 |
missing apostrophe
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| Mar 2, 2014 at 3:42 | answer | added | Jason Starr | timeline score: 6 | |
| Mar 1, 2014 at 8:19 | history | asked | Piotr Achinger | CC BY-SA 3.0 |