Compact moduli of hyperplane arrangements

Details Compact moduli of hyperplane arrangements Compact moduli of hyperplane arrangements

2003-10-30

arxiv.org/abs/math/0310479v1

Mathematics

Algebraic Geometry

27 pages

Scientific paper

The minimal model program suggests a compactification of the moduli space of hyperplane arrangements which is a moduli space of stable pairs. Here, a stable pair consists of a scheme X which is a degeneration of projective space and a divisor D=D_1+..+D_n on X which is a limit of hyperplane arrangements. For example, in the 1-dimensional case, the stable pairs are stable curves of genus 0 with n marked points. Kapranov has defined an alternative compactification using his Chow quotient construction, which may be described fairly explicitly. We prove that these two compactifications coincide. We deduce a description of all stable pairs.

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