Timeline for Deformation of a family of curves in a surface
Current License: CC BY-SA 3.0
15 events
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| Nov 24, 2013 at 1:51 | comment | added | Jack Huizenga | Assuming the base $B$ of your family is irreducible and not a point (and not a constant family), the answer is always no. The curves in $B$ sweep out an irreducible surface, and the curves in $U$ sweep out a dense subset of that surface. | |
| Nov 23, 2013 at 14:55 | history | edited | Naga Venkata | CC BY-SA 3.0 |
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| Nov 23, 2013 at 14:33 | comment | added | Naga Venkata | @Huizenga: Sorry, I meant open subset of $B$. | |
| Nov 23, 2013 at 14:31 | history | edited | Naga Venkata | CC BY-SA 3.0 |
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| Nov 23, 2013 at 5:46 | comment | added | Jack Huizenga | Your (1) seems like nonsense to me. First of all, open neighborhood of $B$ in what? Second of all, curves corresponding to points of $U$ will either sweep out $X$ (if $U$ only parameterizes curves in $X$) or a dense subset of projective space. | |
| Nov 23, 2013 at 4:09 | comment | added | Naga Venkata | @quim: The language in the question has been totally modified. | |
| Nov 23, 2013 at 4:09 | history | edited | Naga Venkata | CC BY-SA 3.0 |
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| Nov 21, 2013 at 2:50 | history | edited | Naga Venkata |
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| Nov 20, 2013 at 19:08 | history | edited | Naga Venkata | CC BY-SA 3.0 |
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| Nov 20, 2013 at 15:56 | comment | added | Naga Venkata | @quim: yes. I am asking whether there exist at least one non-trivial deformation of $S$ which contains all the elements of $U$. We however can take $U$ small enough if it helps. | |
| Nov 20, 2013 at 14:59 | comment | added | quim | Do you mean, for each divisor in U there is a deformation of S which contains it? | |
| Nov 20, 2013 at 13:53 | comment | added | Naga Venkata | @quim: The motivations is as follows: Given a linear system in a surface does there exists "small" deformations of the surface which contains an open subset of the linear system. As for the other questions: We can assume $Hilb_{P,Q}$ irreducible or take an irreducible component in here. | |
| Nov 20, 2013 at 13:42 | comment | added | quim | Probably it would help to get answers if you give some motivation for the question (what are you after? which kind of conditions would be ok in your setting?) Something that confuses me: are you assuming Hilb_{P,Q} irreducible? If so, what does this imply on the pair, (P,Q)? Otherwise, what does "a general element" mean? | |
| Nov 20, 2013 at 9:02 | history | edited | Naga Venkata | CC BY-SA 3.0 |
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| Nov 20, 2013 at 8:54 | history | asked | Naga Venkata | CC BY-SA 3.0 |