Freeness in families of arrangements

Establish a general theorem determining whether non-freeness of the fibers of a family of hyperplane arrangements implies non-freeness of the total-space divisor, particularly for nontrivial families such as the family of generic arrangements of five planes in C^3 parametrized by their two-dimensional moduli space.

Background

Near a generic rank-two matrix, D_{3,5} is described as a nontrivial family of ten-plane arrangements in C^3. Each fiber is non-free, but the paper emphasizes that fiberwise non-freeness does not formally imply non-freeness of the total space when the family is analytically nontrivial.

The specific D_{3,5} case is settled by direct computation, and a related family of generic five-plane arrangements is also found computationally to be non-free along a specified locus. What remains unresolved is a general principle connecting fiberwise and total-space freeness.