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Dear colleagues,

Could you give me a reference (not a proof:) to the following folklore result. If $X\subset\mathbb P^n$ is a smooth irreducible projective variety of dimension $>1$, then any hyperplane section of $X$ is connected. The base field is algebraically closed, characteristic is arbitrary.

Thank you in advance, Serge

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1  
en.wikipedia.org/wiki/… –  Vivek Shende May 18 '13 at 17:33
    
@Vivek. Wow, I had now idea that even this is on Wiki:) Thanks, I will look up the paper. –  Serge Lvovski May 18 '13 at 17:45
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The Fulton-Hansen theory is more general, but this particular case is the Lemma of Enriques-Severi-Zariski, which is older. –  Jason Starr May 18 '13 at 18:40
    
@jason. Thanks! Could you give an explicit reference? –  Serge Lvovski May 18 '13 at 18:50
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( Hartshorne, Algebraic Geometry, Springer, GTM 52, Cor. 7.9, p. 244 ) –  Damian Rössler May 19 '13 at 6:35

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