Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

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
Email: paul.hacking@yale.edu

Sean Keel
Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
Email: keel@math.utexas.edu

Jenia Tevelev
Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
Email: tevelev@math.utexas.edu

DOI: https://doi.org/10.1090/S1056-3911-06-00445-0
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

American Mathematical Society