Timeline for smooth projective curve
Current License: CC BY-SA 2.5
13 events
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| Dec 11, 2010 at 4:47 | comment | added | roy smith | (maybe Z surjects onto f(C), instead of "phi surjective".) | |
| Dec 11, 2010 at 4:37 | comment | added | roy smith | Sandor, forgive me for possibly causing you to delete yours, since I thought it the best possible answer to the case where g,h are not necessarily constant. I.e. there are three situations of possible interest, answered by the union of the criteria we gave: Z non empty (g,h arbitrary), Z contains a curve (g non constant), and phi surjective (both g,h non constant). (Subject to my introduced errors.) | |
| Dec 10, 2010 at 23:05 | comment | added | roy smith | I figured as much, Matt. And I would guess the case of h non constant is the one most interesting to the original questioner as well. But since you had already given the best possible non trivial answer, I had fun with the trivial ones!, regards, roy. | |
| Dec 10, 2010 at 22:50 | history | edited | roy smith | CC BY-SA 2.5 |
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| Dec 10, 2010 at 19:35 | comment | added | Emerton | Dear Roy, I'm not sure whether "Your" in your second sentence applies to me, to the author of the question, to Sandor, or to someone else, but just in case: I misread the question and took it to be asking that $h$ should be non-constant as well as $g$. Thus I required that the image of $f$ be contained in the image of $\phi.$ Regards, Matt | |
| Dec 10, 2010 at 19:27 | comment | added | Sándor Kovács | Dear Roy, this is a reply to your comment to my post that I just deleted. You are right, it was constant. And I knew that. I just realized that I did not read the question completely, and somehow I missed the requirement of being non-constant. That is an obvious thing to ask for and I did wonder about that. I still did not realize that the question asked for that. I guess I read selectively. :( | |
| Dec 10, 2010 at 19:19 | comment | added | mdeland | Yes it does seem right. But presumably Yashica is interested in how to construct these smooth curves C' in X_C dominating C rather than this degenerate case.... | |
| Dec 10, 2010 at 19:04 | history | edited | roy smith | CC BY-SA 2.5 |
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| Dec 10, 2010 at 18:31 | history | edited | roy smith | CC BY-SA 2.5 |
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| Dec 10, 2010 at 18:17 | history | edited | roy smith | CC BY-SA 2.5 |
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| Dec 10, 2010 at 18:12 | history | edited | roy smith | CC BY-SA 2.5 |
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| Dec 10, 2010 at 17:58 | history | edited | roy smith | CC BY-SA 2.5 |
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| Dec 10, 2010 at 17:52 | history | answered | roy smith | CC BY-SA 2.5 |