Timeline for Small Question about the construction of closed subscheme.
Current License: CC BY-SA 3.0
6 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Mar 8, 2012 at 1:47 | comment | added | Choa | Thanks for your kind check with Macaulay. Donu also mentioned about twisting, and I think so too. Sandor worked on a projective 3 space, whick makes the variable $x_2$ vague. On $\mathbb{P^4}$, saturating works with no problem. Again, Thanks! | |
| Mar 8, 2012 at 1:32 | comment | added | Jack Huizenga | Perhaps this is the right way to fix the exercise: instead of looking at $H^i(t,I_t)$, look at $H^i(t,I_t(1))$. This clearly jumps over $t=0$ as there the curve lies in a plane, while it is nondegenerate for other $t$. | |
| Mar 8, 2012 at 1:21 | comment | added | Jack Huizenga | I've been thinking about this for a while, and I'm a little stumped trying to rectify this with Sandor's response. The special fiber should indeed just be the smooth quartic rational curve in $\mathbb{P}^3$, and I don't see where any nilpotents could come from. I think the issue was in fact due to failing to saturate the ideal, so that your description of the ideal didn't actually provide generators for the ideal in the local charts he was working. Playing around in Macaulay, I can't get any of the cohomology groups to jump whatsoever. | |
| Mar 8, 2012 at 0:21 | history | edited | Choa | CC BY-SA 3.0 |
added 13 characters in body
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| Mar 7, 2012 at 23:57 | history | asked | Choa | CC BY-SA 3.0 |