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Topology of arrangements and position of singularities

Enrique Artal Bartolo (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

This work contains an extended version of a course given in Arrangements in Pyrénées. School on hyperplane arrangements and related topics 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)...

Toric and tropical compactifications of hyperplane complements

Graham Denham (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

These lecture notes survey and compare various compactifications of complex hyperplane arrangement complements. In particular, we review the Gel ' fand-MacPherson construction, Kapranov’s visible contours compactification, and De Concini and Procesi’s wonderful compactification. We explain how these constructions are unified by some ideas from the modern origins of tropical geometry.

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