Re: Fibers question. Algebraic Geometry

From: Jannick (odel2000_at_web.de)
Date: 07/24/04 

Date: Sat, 24 Jul 2004 23:03:10 +0200

It cannot happen due to Chavelley's semicontinuity theorem for morphisms of
finite type; it states that the map $x\maptsto\dim_x f^{-1}(f(x))$ for a
morphism $f:X\to Y$ locally of finite type is upper semi-continuous.

"Stein A. Stromme" <stromme@mi.uib.no> schrieb im Newsbeitrag
news:cdhpta$hsa$1@news.ks.uiuc.edu...
> [Jesus Rogelio Perez Buendia]
>
> | HI all,
> |
> | If X and Y are algebraic sets and V C X x Y is algebraic also.
> | And p:X x Y --->X is the projection.
> |
> | Which conditions do I need to have that all the fibers p^(-1)(a)
> | in V has the same dimension? More accurate: When do we have a pont
> | a in X such that de fiber of a in V has dimension < than the generic
> | fiber?
>
> If p is proper, e.g. if Y is projective, this cannot happen at all.
>
> SA
> --
> Stein Arild Strømme +47 55584825, +47 95801887
> Universitetet i Bergen Fax: +47 55589672
> Matematisk institutt www.mi.uib.no/stromme/
> Johs Brunsg 12, N-5008 BERGEN stromme@mi.uib.no
>