Re: projection in projective varieties
- From: Kira Yamato <kirakun@xxxxxxxxxxxxx>
- Date: Wed, 15 Nov 2006 19:46:12 GMT
On 2006-11-15 13:59:06 -0500, Kira Yamato <kirakun@xxxxxxxxxxxxx> said:
I asked a similar question before. Basically, there's a result that says
the image of a projective variety under a morphism of projective spaces is closed.
So, the projection here is such morphism. So, the image of X must be closed too. The only closed sets in P^1 are P^1 itself and sets of finite discrete points. Moreover, X is irreducible, so the image must be irreducible too. So, the only possibilities are P^1 and single points. Lastly, it's not difficult to show examples where both cases can occur.
Oh wait... I'm not sure what I just said made sense at all. Let me think it over....
--
-kira
.
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