We consider Kapranov's Chow quotient compactification of the moduli space of ordered $n$ -tuples of hyperplanes in $P^{r-1}$ in linear general position. For $r=2$ , this is canonically identified with the Grothendieck-Knudsen compactification of $M_{0,n}$ 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 $(r,n)$ , but we show that (3), which we view as the deepest, fails except possibly in the cases $(2,n)$ , $(3,6)$ , $(3,7)$ , $(3,8)$ , where we conjecture that it holds