From: lrudolph@panix.com (Lee Rudolph)
Subject: Re: Hypersurface in C^2
Date: 16 Apr 2001 12:58:30 -0400
Newsgroups: sci.math
Summary: Complements of complex curves are connected

olaveshta@REMOVEmy-deja.com (Ola Veshta) writes:

>Let p(x,y) be a complex polynomial in x,y , S the hypersurface 
>p(x,y) = 0 in C^2 and A the complement of S in C^2.
>Is it true that for every such p(x,y) the set A is connected ?

Yes (with the single exception of p identically 0).
 
In fact, given two points in C^2, the complex line that they determine 
either is contained in S or contains only finitely many points of S;
so given two points of A, they can be joined by a real arc in the
complex line they determine.

Lee Rudolph