Zero-divisors-cup-length conjecture for hyperplane arrangement complements

Let an arrangement of finitely many complex central hyperplanes have complement $M$. Let the zero-divisors-cup-length of $H^*(M,\mathbf C)$ mean the largest number of zero-divisors in the cohomology of $M$ whose product is nonzero. Zero-divisors-cup-length conjecture. The topological complexity satisfies

$$\operatorname{TC}(M)=\text{the zero-divisors-cup-length of }H^*(M,\mathbf C)+1.$$

For the hyperplane arrangement complements considered in the paper, the computed topological complexity agrees with this lower bound, motivating the conjecture for every complex central hyperplane arrangement.