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Jul 12, 2011 at 6:54 vote accept gio
Jul 11, 2011 at 17:20 comment added Karl Schwede gio, another point you can consider is what do you mean by $E = \beta^{-1}(Z)$. Do you mean scheme theoretically, or set theoretically. In particular, does $E$ have the reduced structure? That's how I interpreted your question in my answer. If not, then the thing you wanted is still not true, but there might be a little more hope in some examples.
Jul 11, 2011 at 15:43 comment added gio Thank you for your answer. Hence what I wanted would be valid only if $E$ is irreducible. I think also that find conditions of $Z$ to ensure the irreducibility of $E$ is very complicated :(... bye
Jul 11, 2011 at 13:54 history answered Karl Schwede CC BY-SA 3.0