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On representation varieties of Artin groups,projective arrangements and the fundamental groups of smooth complex algebraic varieties.
RANDOM WALKS AND HYPERPLANE ARRANGEMENTS
Random Walks and Plane Arrangements in Three Dimensions.
Abstract: We show that the monodromy operator action on the first cohomology group of the Milnor fiber is combinatorially determined for line arrangements with at most triple points and containing at ...
Abstract: In this paper we show that to each planar line arrangement defined over the real numbers, for which no two lines are parallel, one can write down a corresponding relation on Dehn twists that...
A necessary and sufficient condition for the triviality of the Milnor monodromy of a central hyperplane arrangement is given. This is a consequence of a Thom-Sebastiani type result, where the sum of h...
Let W be a finite Weyl group and A be the corresponding Weyl arrangement. A deformation of A is an affine arrangement which is obtained by adding to each hyperplane H ∈ A several parallel trans-lation...
We give a necessary and sufficient condition in order for a hyperplane arrangement to be of Torelli type, namely that it is recovered as the set of unstable hyperplanes of its Dolgachev sheaf of loga...
Using the classification of finite Weyl groupoids we prove that crystallographic arrangements, a large subclass of the class of simplicial arrangements which was recently defined, are hereditarily in...
Let $\A$ be an irreducible Coxeter arrangement and $W$ be its Coxeter group. Then $W$ naturally acts on $\A$. A multiplicity $\bfm : \A\rightarrow \Z$ is said to be equivariant when $\bfm$ is constant...
We show that for arrangements of lines with points of multiplicity at most three, the cohomology of Milnor fiber is determined only by the combinatorics of arrangement. The proof depends on enumeratio...
A toric arrangement is a finite set of hypersurfaces in a complex torus,every hypersurface being the kernel of a character. In the present paper we build a CW-complex homotopy equivalent to the arrang...
We show that if the fundamental groups of the complements of two line arrangements in the complex projective plane are isomorphic to the same direct sum of free groups, then the complements of the arr...
We consider hyperplane arrangements generated by generic points and study their intersection lattices. These arrangements are known to be equivalent to discriminantal arrangements. We show a fundament...

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