Re: Fibers question. Algebraic Geometry

From: Stein A. Stromme (stromme_at_mi.uib.no)
Date: 07/25/04 

Date: Sun, 25 Jul 2004 11:44:35 +0200

[Jannick]

| 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.

But the OP wanted the function on the _target_ space. Then the
projection of the hyperbola xy-1 in the affine plane to the x-axis is
clearly an example.

SA

PS: please avoid top posting; it makes your post difficult to read
and the logic of the thread difficult to follow.

====================================================================

|
| "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
| >
|
| 

-- 
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