Compactification of the moduli space of hyperplane arrangements
Authors:
Paul Hacking, Sean Keel and Jenia Tevelev
Journal:
J. Algebraic Geom. 15 (2006), 657-680
DOI:
https://doi.org/10.1090/S1056-3911-06-00445-0
Published electronically:
May 2, 2006
MathSciNet review:
2237265
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Abstract |
References |
Additional Information
Abstract: Consider the moduli space $M^0$ of arrangements of $n$ hyperplanes in general position in projective $(r-1)$-space. When $r=2$ the space has a compactification given by the moduli space of stable curves of genus $0$ with $n$ marked points. In higher dimensions, the analogue of the moduli space of stable curves is the moduli space of stable pairs: pairs $(S,B)$ consisting of a variety $S$ (possibly reducible) and a divisor $B=B_1+\dots +B_n$, satisfying various additional conditions. We identify the closure of $M^0$ in the moduli space of stable pairs as Kapranov’s Hilbert quotient compactification of $M^0$, and give an explicit description of the pairs at the boundary. We also construct additional irreducible components of the moduli space of stable pairs.
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Additional Information
Paul Hacking
Affiliation:
Department of Mathematics, Yale University, P.O. Box 208283, New Haven, Connecticut 06520
MR Author ID:
737867
Email:
paul.hacking@yale.edu
Sean Keel
Affiliation:
Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
MR Author ID:
289025
Email:
keel@math.utexas.edu
Jenia Tevelev
Affiliation:
Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
MR Author ID:
607263
Email:
tevelev@math.utexas.edu
Received by editor(s):
February 9, 2005
Received by editor(s) in revised form:
June 7, 2005
Published electronically:
May 2, 2006
Additional Notes:
The second author was partially supported by NSF grant DMS-9988874