I'm studying algebraic geometry alone. I am a 'Baby'.

I need your help!

On p.199 of Hartshorne's "Algebraic Geometry", what does Ex9.2 tell me??

I even can't prove it.

I want to know the proof or hint, and meaning of it.

Could someone explains this for me, thanks.

  • 13
    $\begingroup$ Why don't you write down the question for people who don't have the book available? $\endgroup$ – Zev Chonoles Feb 27 '11 at 13:38

It can happen that a morphism of schemes $f:X\to Z$ contracts a positive dimensional subscheme $Y\subset X$ to a point $P\in Z$ although $f$ itself is not constant. Do you know an example ? (It is already somewhere in Chapter I of Hartshorne). Do you think this can happen if $X= \mathbb P^n $ ? Reread your exercise. Can you answer now?


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