Papers › Initial degenerations of flag varieties
Initial degenerations of flag varieties
Daniel Corey, Jorge Alberto Olarte
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We prove that the initial degenerations of the flag variety admit closed immersions into finite inverse limits of flag matroid strata, where the diagrams are derived from matroidal subdivisions of a suitable flag matroid polytope. As an application, we prove that the initial degenerations of Fℓ°(n) -- the open subvariety of the complete flag variety Fℓ(n) consisting of flags in general position -- are smooth and irreducible when n≤4. We also study the Chow quotient of Fℓ(n) by the diagonal torus of PGL(n), and show that, for n=4, this is a log crepant resolution of its log canonical model.
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