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Mar 7, 2016 at 6:15 comment added j.c. Thanks for this answer. It appears that the determinant does vanish for some elements of the Grassmannian. I should have checked this earlier. For instance, in the Laplace expansion above, there are several brackets which do not appear ([146], [245], and [356]). Thus the point where e.g. [146] is the only nonvanishing Plucker coordinate is one where the determinant vanishes. I may need some more details for the rest of your answer though I will study the paper you linked.
Mar 7, 2016 at 3:46 history answered dhy CC BY-SA 3.0