Duke Mathematical Journal

Geometry of Chow quotients of Grassmannians

Sean Keel and Jenia Tevelev

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Abstract

We consider Kapranov's Chow quotient compactification of the moduli space of ordered n-tuples of hyperplanes in Pr1 in linear general position. For r=2, this is canonically identified with the Grothendieck-Knudsen compactification of M0,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

Article information

Source
Duke Math. J., Volume 134, Number 2 (2006), 259-311.

Dates
First available in Project Euclid: 8 August 2006

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1155045503

Digital Object Identifier
doi:10.1215/S0012-7094-06-13422-1

Mathematical Reviews number (MathSciNet)
MR2248832

Zentralblatt MATH identifier
1107.14026

Subjects
Primary: 14E
Secondary: 14D 52C35: Arrangements of points, flats, hyperplanes [See also 32S22]

Citation

Keel, Sean; Tevelev, Jenia. Geometry of Chow quotients of Grassmannians. Duke Math. J. 134 (2006), no. 2, 259--311. doi:10.1215/S0012-7094-06-13422-1. https://projecteuclid.org/euclid.dmj/1155045503


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