Motivic zeta functions of hyperplane arrangements

Abstract For each central essential hyperplane arrangement $\mathcal{A}$ over an algebraically closed field, let $Z_\mathcal{A}^{\hat\mu}(T)$ denote the Denef–Loeser motivic zeta function of . We prove a formula expressing in terms Milnor fibers related arrangements. This shows that, precise sense, degree to which $Z_{\mathcal{A}}^{\hat\mu}(T)$ fails be combinatorial invariant is completely controlled by these fibers. As one application, we use this show that map taking complex Hodge–Deligne specialization locally constant on realization space any loop-free matroid. also Igusa characteristic polynomials