Compactification of the moduli space of hyperplane arrangements

Paul Hacking; Sean Keel; Jenia Tevelev

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arXiv · math/0501227

Compactification of the moduli space of hyperplane arrangements

Paul Hacking·Sean Keel·Jenia Tevelev

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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+..+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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BibTeX RIS

Paul Hacking, Sean Keel, Jenia Tevelev. 2005-01-14. Compactification of the moduli space of hyperplane arrangements. https://arxiv.org/abs/math/0501227

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