Initial degenerations of Grassmannians

Daniel Corey ^[1]
1. [1] UW-Madison, USA
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 4, 2021
Idioma: inglés
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Resumen
- We construct closed immersions from initial degenerations of Gr0(d,n)—the open cell in the Grassmannian Gr(d,n) given by the nonvanishing of all Plücker coordinates—to limits of thin Schubert cells associated to diagrams induced by the face poset of the corresponding tropical linear space. These are isomorphisms when (d, n) equals (2, n), (3, 6) and (3, 7). As an application we prove Gr0(3,7) is schön, and the Chow quotient of Gr(3,7) by the maximal torus in PGL(7) is the log canonical compactification of the moduli space of 7 points in P2 in linear general position, making progress on a conjecture of Hacking, Keel, and Tevelev.