2004/01/14 by Seán Keel, Sean Keel, Keel, Sean +2
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG
paper · pdf · doi:10.48550/arxiv.math/0401159
Proofs in section 3 are simplified, some technical details and typos are corrected. The proof of 1.5 is removed - a more general modular result will appear in the joint paper with Paul Hacking
openalex publication_date 2004/01/14 · arxiv created 2004/08/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider Kapranov's Chow quotient compactification of the moduli space of ordered n-tuples of hyperplanes in Pr-1 in linear general position. For r=2 this is canonically identified with the Grothendieck-Knudsen compactification of M0,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.