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Jul 20, 2015 at 2:35 comment added Alexander Woo Sorry - I've told you pretty much everything I know. You might search using 'matroid stratification' also - or hope someone more knowledgeable comes along!
Jul 19, 2015 at 14:52 comment added user71216 Thanks. I did some searching on Mnev's theorem, and see that 3 is certainly hopeless. However, I don't fully understand the theorem since I know nothing about real algebraic geometry. So, when we say arbitrarily nasty things occur, does this include having multiple components of various dimensions?
Jul 18, 2015 at 21:42 comment added Alexander Woo This is the same as the matroid stratification of the Grassmannian (since each Plucker coordinate tells you whether certain rows are dependent or not). Much is known, but Mnev's theorem also says that arbitrarily nasty things occur.
Jul 18, 2015 at 18:14 history asked user71216 CC BY-SA 3.0