Titlebook: Hyperplane Arrangements; An Introduction Alexandru Dimca Textbook 2017 Springer International Publishing AG 2017 hyperplane arrangements.Mi

Commission

夸张

Milnor Fibers and Local Systems,he cohomology .. We recall the definition and some basic properties of rank one local systems, and explain the relation between monodromy eigenspaces and the twisted cohomology of the complement ., where . is the projective arrangement associated to .. Then we state a very general vanishing result f

REP

Characteristic Varieties and Resonance Varieties,. We explain the relation between the characteristic varieties and the homology of finite abelian covers. The polynomial periodicity properties of the first Betti numbers of such covers, and the smooth surfaces obtained as coverings of . ramified over a line arrangement, are also discussed. The main

COW

背景

Free Arrangements and de Rham Cohomology of Milnor Fibers, Criterion in this setting. The factorization property for . when . is a free arrangement, the fact that any supersolvable arrangement is free, and the freeness of reflection arrangements are all stated in the first section. Then we restrict to the case of curves (and in particular, line arrangement

翻布寻找

Characteristic Varieties and Resonance Varieties,ltinet structures introduced by M. Falk and S. Yuzvinsky. After a brief discussion of the translated components of the characteristic varieties, we treat in great detail the deleted .-line arrangement.

radiograph

Free Arrangements and de Rham Cohomology of Milnor Fibers,ral sequence approach to the computation of the Alexander polynomial of a plane curve. Two algorithms are described, one for free plane curves, the other for curves in . having only weighted homogeneous singularities.

Enervate

Hyperplane Arrangements and Their Combinatorics,ial of an arrangement. These polynomials enter into Zaslavsky’s Theorem expressing the number of regions (resp. bounded regions) of the complement of a real arrangement. In this chapter we also introduce several important classes of hyperplane arrangements: the supersolvable arrangements, the graphic arrangements and the reflection arrangements.

Gratulate

,Orlik–Solomon Algebras and de Rham Cohomology,which says that the topology is often determined by the combinatorics. A tensor product decomposition of the Orlik–Solomon algebra of a supersolvable arrangement, as well as an alternative view of the Orlik–Solomon algebra of a projective hyperplane arrangement, can also be found here.

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