Timeline for Can a surface of the following type contain a line?
Current License: CC BY-SA 3.0
8 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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| Dec 3, 2011 at 4:18 | comment | added | Stanley Yao Xiao | Would the existence of a rational curve in a surface imply the existence of many rational solutions? | |
| Nov 30, 2011 at 15:14 | comment | added | Felipe Voloch | But in weighted projective space what do you mean by a line? Just a rational curve? | |
| Nov 30, 2011 at 14:58 | comment | added | Stanley Yao Xiao | Yes; I do mean a surface in weighted projective space. | |
| Nov 30, 2011 at 14:58 | history | edited | Stanley Yao Xiao | CC BY-SA 3.0 |
added 31 characters in body
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| Nov 30, 2011 at 1:10 | comment | added | Jason Starr | You can consider it as a surface in a weighted projective space $\mathbb{P}(a,a,b,b)$ such that $a\text{deg}(f)$ equals $b\text{deg}(g)$ (and probably best to assume that $a$ and $b$ are relatively prime). | |
| Nov 29, 2011 at 23:25 | comment | added | Daniel Loughran | Unless I am mistaken, one cannot view what you have written down ($f(x_1,x_2)=g(x_3,x_4)$) as a being a surface unless $f$ and $g$ are homogeneous of the same degree, and also in which case you need to consider the corresponding variety as being projective. | |
| Nov 29, 2011 at 22:57 | history | asked | Stanley Yao Xiao | CC BY-SA 3.0 |