Diffeomorphic types of the complements of arrangements of hyperplanes

Tan Jiang; Stephen S.-T. Yau

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This work contains an extended version of a course given in held at Pau (France) in June 2012. In the first part, we recall the computation of the fundamental group of the complement of a line arrangement. In the second part, we deal with characteristic varieties of line arrangements focusing on two aspects: the relationship with the position of the singular points (relative to projective curves of some prescribed degrees) and the notion of essential coordinate components.