Timeline for Connecting points on a variety by the image of a nonsingular curve
Current License: CC BY-SA 3.0
7 events
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| Sep 13, 2011 at 20:06 | comment | added | HNuer | @jlk Also in order for your assertion that the general section meets the fibers $f^{-1}(x)$ and $f^{-1}(y)$ from a dimension count, I believe you also need that dim $X\geq 2$. You don't just need it to define the blow-up, unless you had some other dimensional reason in mind, which I'd like to here. Thanks for the nice answer. | |
| Sep 13, 2011 at 19:36 | comment | added | jlk | @MP: Your remark reminded me that in my proof sketch, I should have stated at the beginning "We can assume the dimension of $X$ is at least $2$." No suitable blow-up exists if $X$ is a single point... | |
| Sep 13, 2011 at 19:35 | history | edited | jlk | CC BY-SA 3.0 |
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| Sep 13, 2011 at 16:23 | comment | added | M P | Maybe less tautologically: if the singular locus of $X$ is the support of an ample divisor, then you are probably in trouble. | |
| Sep 13, 2011 at 16:22 | comment | added | M P | To answer your question: if $X$ is itself a singular curve! | |
| Sep 13, 2011 at 16:18 | history | edited | jlk | CC BY-SA 3.0 |
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| Sep 13, 2011 at 16:11 | history | answered | jlk | CC BY-SA 3.0 |