The reduction map for the moduli spaces of weighted stable hyperplane arrangements

Abstract Alexeev constructed moduli spaces of weighted stable hyperplane arrangements generalizing the Hasset's moduli space of curves of genus 0 with weighted $n$ points. For curves, the reduction map $overline{M}_{beta}(2,n)rightarrowoverline{M}_{beta'}(2,n)$ is surjective for any weights $betagebeta'$. We study first a combinatorial statement about tilings which is related to the surjectivity of the reduction map for Alexeev's space when $n=5,6,7,8,9$. . We will show there is a counterexample to the combinatorial statement when n=10 , which works as a counter-example to the surjectivity of the reduction map for Alexeev's space when n=10 .