Titlebook: Arrangements, Local Systems and Singularities; CIMPA Summer School, Fouad Zein,Alexandru I. Suciu,Sergey Yuzvinsky Conference proceedings 2

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John F. Holzrichter,Kenneth R. ManesThe article describes local systems, integrable connections, the equivalence of both categories and their relations to linear differential equations. We report in details on regular singularities of connections and on singularities of local systems which leads to the theory of intermediate extensions and the decomposition theorem.

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Paul James Cardwell,Tamara HerveyWe give an elementary introduction of the toric modification, using an irreducible plane curve germ. We explain also the relation between the tower of the toric modifications which gives a resolution of the curve and the Puiseux pairs.

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Combinatorics of Covers of Complexified Hyperplane Arrangements,This is a survey of combinatorial models for covering spaces of the complement of a complexified hyperplane arrangement. We obtain a unified picture of the subject, and a generalization of various known results, by exploiting the toolkit of homotopy colimits for combinatorial applications developed by Welker, Ziegler and Živaljević.

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Problem Session,This article contains the open problems posed at the special session of the CIMPA summer school “Arrangements, Local Systems and Singularities” held at Galatasaray University, İstanbul, 2007.

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