We consider Kapranov's Chow quotient compactification of the moduli space of ordered -tuples of hyperplanes in in linear general position. For , this is canonically identified with the Grothendieck-Knudsen compactification of which has, among others, the following nice properties:
(1) modular meaning: stable pointed rational curves;
(2) canonical description of limits of one-parameter degenerations;
(3) natural Mori theoretic meaning: log-canonical compactification.
We generalize (1) and (2) to all , but we show that (3), which we view as the deepest, fails except possibly in the cases , , , , where we conjecture that it holds
Sean Keel. Jenia Tevelev. "Geometry of Chow quotients of Grassmannians." Duke Math. J. 134 (2) 259 - 311, 15 August 2006. https://doi.org/10.1215/S0012-7094-06-13422-1