In geometry and combinatorics an arrangement of hyperplanes is an arrangement of a finite set a of hyperplanes in a linear affine or projective space squestions about a hyperplane arrangement a generally concern geometrical topological or other properties of the complement ma which is the set that remains when the hyperplanes are removed from the whole space. An introduction to hyperplane arrangements 1 lecture 1 basic de nitions the intersection poset and the characteristic polynomial 2 exercises 12 an arrangement of linear hyperplanes ie hyperplanes passing through the origin many other writers call an arrangementcentral rather than linear if 0 2 t. Examples of arrangements of hyperplanes 1 a subset of the coordinate hyperplanes is called a boolean arrangement 2 an arrangement is in general position if at each point it is locally boolean 3 the braid arrangement consists of the hyperplanes it is the set of reflecting hyperplanes of the . An arrangement of hyperplanes is a finite collection of codimension one affine subspaces in a finite dimensional vector space arrangements have emerged independently as important objects in various fields of mathematics such as combinatorics braids configuration spaces representation theory reflection groups singularity theory and in computer science and physics. The modern study of arrangements of hyperplanes started in the early 1980s since the object of study is simple just a finite set of hyperplanes there are various mathematical approaches to arrangements including algebra topology combinatorics singularities integral systems hypergeometric functions and statistics
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