Given a representable morphisms $f:\mathcal{X}\to\mathcal{Y}$ of Artin stacks, do the fibers of $f$ have always nonnegative dimension? If not, can you give me some examples of what can happen?
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$\begingroup$ It is not true. The identity map is a representable morphism whose fibers have dimension zero. $\endgroup$– PassengerCommented Mar 24, 2011 at 9:05
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$\begingroup$ sorry, I meant nonnegative dimension $\endgroup$– ginevra86Commented Mar 24, 2011 at 9:05
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8$\begingroup$ Yes, the fibers are algebraic spaces. $\endgroup$– Laurent Moret-BaillyCommented Mar 24, 2011 at 9:07
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7$\begingroup$ What is the dimension of the empty algebraic space? $\endgroup$– Torsten EkedahlCommented Mar 24, 2011 at 9:35
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2$\begingroup$ Good point, Torsten. The fibers have nonnegative dimension everywhere. $\endgroup$– Laurent Moret-BaillyCommented Mar 24, 2011 at 12:58
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