Duke Mathematical Journal
- Duke Math. J.
- Volume 134, Number 2 (2006), 259-311.
Geometry of Chow quotients of Grassmannians
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
Duke Math. J., Volume 134, Number 2 (2006), 259-311.
First available in Project Euclid: 8 August 2006
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Secondary: 14D 52C35: Arrangements of points, flats, hyperplanes [See also 32S22]
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