Complex spaces with a global holomorphic function being a zero divisor in a local ring - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T01:24:44Z http://mathoverflow.net/feeds/question/100567 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/100567/complex-spaces-with-a-global-holomorphic-function-being-a-zero-divisor-in-a-local Complex spaces with a global holomorphic function being a zero divisor in a local ring Alex 2012-06-25T05:49:58Z 2012-06-25T12:26:45Z <p>Is there a simple example of a complex space $X$ with the following property: there is a function $f$ holomorphic on $X$ such that: (i) $f$ is not a zero divisor in the ring ${\mathcal O}(X)$ of all functions holomorphic on $X$; (ii) $f$ is a zero divisor in the local ring ${\mathcal O}_x(X)$ for some point $x\in X$? </p>