Milnor fibers of real line arrangements

Journal of Singularities
volume 7 (2013), 220-237

Received: 13 June 2013.

DOI: 10.5427/jsing.2013.7l

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Abstract:

We study Milnor fibers of complexified real line arrangements. We give a new algorithm computing monodromy eigenspaces of the first cohomology. The algorithm is based on the description of minimal CW-complexes homotopic to the complements, and uses the real figure, that is, the adjacency relations of chambers. It enables us to generalize a vanishing result of Libgober, give new upper-bounds and characterize the A_3-arrangement in terms of non-triviality of Milnor monodromy.

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