Chow Quotients of Grassmannians II

Details Chow Quotients of Grassmannians II Chow Quotients of Grassmannians II

2004-01-14

arxiv.org/abs/math/0401159v5

Mathematics

Algebraic Geometry

Proofs in section 3 are simplified, some technical details and typos are corrected. The proof of 1.5 is removed - a more gener

Scientific paper

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 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 prove (1-2) generalize naturally to all (r,n), but 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 it holds. The same generalization of (1) was given recently (and independently) by Hacking.

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