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Nov 15, 2013 at 22:39 vote accept jacob
Nov 14, 2013 at 10:43 answer added Olivier Benoist timeline score: 5
Nov 12, 2013 at 12:40 comment added Jason Starr Blow down some lines on a quintic threefold. This gives singular, proper, three-dimensional algebraic spaces that have the pathological property you describe.
Nov 12, 2013 at 8:00 comment added Sándor Kovács Hironaka's example satisfies this condition, because it maps onto a projective variety of positive dimension. (See my answer below).
Nov 12, 2013 at 8:00 answer added Sándor Kovács timeline score: 3
Nov 12, 2013 at 7:09 comment added abx Have you looked at Hironaka's example? It contains some pairs of points which are not contained in any affine open subset, they would be good candidates for your $P,Q$.
Nov 12, 2013 at 5:49 history asked jacob CC BY-SA 3.0