Timeline for Family of curve singularities whose generic members are smooth
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26 events
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| Jun 15, 2021 at 21:39 | history | edited | YCor | CC BY-SA 4.0 |
fixed typo, added tag
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| Jun 15, 2021 at 21:08 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Feb 15, 2021 at 21:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jan 16, 2021 at 20:55 | answer | added | Juan Nuno-Ballesteros | timeline score: 0 | |
| Feb 16, 2014 at 11:22 | comment | added | Trinh | Thanks Artie. I think for this situation what you have said is true. I shall ask something relating to this topic later (for morphisms whose special fiber has some ebedded points, but its delta-invariant is zero like the delta-invariant of the generic fibers). Thanks again. | |
| Feb 14, 2014 at 9:03 | comment | added | user5117 | @Trinh: take the point $p$ in the base over which you have a multiple fibre, and take a neighbourhood of $p$ (in whatever sense you like). | |
| Feb 14, 2014 at 4:58 | comment | added | Trinh | The example of elliptic pencil on an Enriques surface is a counter example of my question in the global case. Thanks Artie Prendergast-Smith and Alex Degtyarev. However, what I am looking for is in local situation, that is, looking for a local family of curve singularities with such a property. | |
| Feb 14, 2014 at 4:52 | comment | added | Trinh | Dear @Artie: I used "curve singularities" to remark that all fibers should be of dimension 1. Of course, if $X$ is pure dimensional then the generic fiber $X_t$ has no isolated points, and $X_t$ is purely 1-dimensional, then I schould just enough to write "smooth". | |
| Feb 13, 2014 at 18:49 | review | First posts | |||
| Feb 13, 2014 at 19:11 | |||||
| Feb 13, 2014 at 16:52 | comment | added | Alex Degtyarev | To be more precise, e.g., any elliptic pencil on an Enriques surface. | |
| Feb 13, 2014 at 16:10 | comment | added | user5117 | Dear @user46910, I suppose I am objecting to saying that a smooth fiber is a "curve singularity". That seems needlessly complicated --- why not just say it is smooth? About your question, I am asserting there are fibred surfaces where the generic fibre is smooth, but some (scheme-theoretic) fibre is nowhere reduced. Is that the kind of example you are looking for? | |
| Feb 13, 2014 at 16:06 | comment | added | Trinh | @Artie: $f:X \rightarrow T$ has smooth generic fibers who all are curve singularities. The special fiber maybe not smooth, but my question is, whether the smoothness of the generic fibers ensure for the reducedness of the special fiber (together with the pure-dimensionality of $X$, i.e., the generic fibers has no isolated points)? | |
| Feb 13, 2014 at 15:42 | comment | added | user5117 | Also, the phrase "smooth curve singularities" is confusing; do you mean that the fibers are smooth? | |
| Feb 13, 2014 at 15:38 | comment | added | user5117 | I think I am misunderstanding the question: what about e.g. elliptic surfaces with multiple fibres? | |
| Feb 13, 2014 at 15:13 | history | asked | Trinh | CC BY-SA 3.0 |