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I would like to understand when a toric variety is connected. Given $\Delta$ a fan (possibly with infinitely many cones) in $\mathbb{R}^n$, $n\geq 2$ denote with $X_{\Delta}$ the associated toric variety. I would like to know if there exists some property $P$ for which a theorem as follows holds:

if $\Delta$ satisfies $P$ then $X_{\Delta}$ is connected.

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margarida? :) sei tu? – diverietti Jun 16 '13 at 16:02
I don't even understand what it would mean for a disconnected variety to be toric. – Dan Petersen Jun 16 '13 at 16:42
With the definition I know, every toric variety is connected. – Angelo Jun 16 '13 at 17:00
The usual definition of "fan" implies that every two cone intersect in a common (non-empty) sub-cone: which implies that the open sets corresponding to those cones intersect in a non-empty open set. So the toric variety is connected by default. – auniket Jun 16 '13 at 18:18
Wait... we will again have to discuss whether or not the empty scheme is connected. – Fred Rohrer Jun 16 '13 at 20:35

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