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Apr 11, 2017 at 13:03 vote accept john mangual
Jan 26, 2012 at 14:10 comment added B. Bischof David's comment, and Jack's answer are really what you are looking for. However, since you brought up Schubert Calculus specifically, let me point you at this paper:arxiv.org/pdf/math/0608784v1.pdf by Ronga, which talks about a more classical perspective on the Schubert calculus. In fact, in this paper, you can see a picture similar to yours about configuration of lines. I think this purely expository paper gives a very beautiful picture of the incidence geometry.
Jan 26, 2012 at 5:22 answer added Jack Huizenga timeline score: 6
Jan 26, 2012 at 5:15 comment added David Eppstein My feeling is that this should be simpler in the projective plane than in the Euclidean plane — arrangements of lines in the Euclidean plane as you are trying to classify are basically arrangements of lines in the projective plane where you have one more line and you have fixed it at infinity, so the two theories aren't really different, but when you look at it projectively you don't have to make a distinction between triple intersections and parallel lines, they become the same thing.
Jan 26, 2012 at 2:52 history asked john mangual CC BY-SA 3.0