Compactification of the moduli space of hyperplane arrangements

Details Compactification of the moduli space of hyperplane arrangements Compactification of the moduli space of hyperplane arrangements

2005-01-14

arxiv.org/abs/math/0501227v1

J. Algebraic Geom. 15 (2006), 657--680

Mathematics

Algebraic Geometry

26 pages, 1 figure

Scientific paper

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+..+B_n, satisfying various additional assumptions. We identify the closure of M^0 in the moduli space of stable pairs as Kapranov's Chow 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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