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首页> 外文期刊>Mathematical Proceedings of the Cambridge Philosophical Society >Motivic zeta functions of hyperplane arrangements
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Motivic zeta functions of hyperplane arrangements

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摘要

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

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