Re: What are variety morphisms?
- From: Hagen <knaf@xxxxxxxxxxx>
- Date: Wed, 03 May 2006 06:19:30 EDT
In Hartshorne's Algebraic Geometry book Chapter 1, he
defines a morphism
T:X->Y of varieties to be a
1) continuous (Zariski) map
such that
2) for every open set W in Y and every regular
function f on W, the
composition fT is regular on T^(-1)(W) in X.
I'm trying to understand why he required both
conditions 1) and 2).
Hartshorne did give an example of a map that is 1)
but not 2). Is there
an example that is 2) but not 1)?
-kira
First hand without requiring T^(-1)(W) to be a topologically >>nice<< set one has problems in
defining what regular means for a function on that
set.
H
.
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