TGiZ-Seminar: Tropical geometry in Zoom (Third meeting Summer Semester 2022)
Daniel Corey (Technische Universität Berlin)

Abstract: We prove that the initial degenerations of the type-A 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_0(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. This is based on joint work with Jorge Alberto Olarte.