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Complements of Hypersurfaces, Variation Maps, and Minimal Models of Arrangements

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Bridging Algebra, Geometry, and Topology

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 96))

Abstract

We prove the minimality of the CW-complex structure for complements of hyperplane arrangements in C n by using the theory of Lefschetz pencils and results on the variation maps within a pencil of hyperplanes. This also provides a method to compute the Betti numbers of complements of arrangements via global polar invariants.

To Alexandru Dimca and Ştefan Papadima, on the occasion of a great anniversary

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Authors and Affiliations

  1. Mathématiques, UMR 8524 CNRS, Université Lille 1, 59655, Villeneuve d’Ascq, France

    Mihai Tibăr

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  1. Mihai Tibăr
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Correspondence to Mihai Tibăr .

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Editors and Affiliations

  1. Faculty of Mathematics and Informatics, Ovidius University, Constanta, Constanta, Romania

    Denis Ibadula

  2. Department of Mathematics, University of Leuven, Leuven (Heverlee), Belgium

    Willem Veys

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Tibăr, M. (2014). Complements of Hypersurfaces, Variation Maps, and Minimal Models of Arrangements. In: Ibadula, D., Veys, W. (eds) Bridging Algebra, Geometry, and Topology. Springer Proceedings in Mathematics & Statistics, vol 96. Springer, Cham. https://doi.org/10.1007/978-3-319-09186-0_18

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