Compactification of the moduli space of hyperplane arrangements

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Consider the moduli space M⁰ 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=B₁+..+Bₙ, satisfying various additional assumptions. We identify the closure of M⁰ in the moduli space of stable pairs as Kapranov's Chow quotient compactification of M⁰, and give an explicit description of the pairs at the boundary. We also construct additional irreducible components of the moduli space of stable pairs.