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Degeneration of Orlik–Solomon algebras and Milnor fibers of complex line arrangements

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Abstract

We give a vanishing theorem for the monodromy eigenspaces of the Milnor fibers of complex line arrangements. By applying the modular bound of the local system cohomology groups given by Papadima–Suciu, the result is deduced from the vanishing of the cohomology of certain Aomoto complex over finite fields. In order to prove this, we introduce degeneration homomorphisms of Orlik–Solomon algebras.

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Acknowledgments

The authors thank Professor Alexandru Dimca for his suggestions and encouragements. The second author is supported by JSPS Grant-in-Aid for Scientific Research (C) 25400060.

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Authors and Affiliations

  1. Laboratoire J.A. Dieudonné UMR CNRS 7351, Université de Nice Sophia-Antipolis Parc Valrose, 06108, Nice Cedex 02, France

    Pauline Bailet

  2. Department of Mathematics, Hokkaido University, North 10, West 8, Kita-ku, Sapporo, 060-0810, Japan

    Pauline Bailet & Masahiko Yoshinaga

Authors
  1. Pauline Bailet
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  2. Masahiko Yoshinaga
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Correspondence to Masahiko Yoshinaga.

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Bailet, P., Yoshinaga, M. Degeneration of Orlik–Solomon algebras and Milnor fibers of complex line arrangements. Geom Dedicata 175, 49–56 (2015). https://doi.org/10.1007/s10711-014-0027-7

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  • DOI: https://doi.org/10.1007/s10711-014-0027-7

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