Moduli space of combinatorially equivalent arrangements of hyperplanes and logarithmic Gauss–Manin connections

We consider a moduli space of combinatorially equivalent family of arrangements of hyperplanes (e.g., n distinct points in the complex line). A compactification of the moduli space is obtained by adding a boundary divisor. On the moduli space we study a Gauss–Manin connection and show that it has logarithmic poles along the boundary divisor. When the moduli space is one-codimensional, an explicit formula for the connection matrix is given.