The twisted de Rham cohomology for basic constructionsof hyperplane arrangements and its applications

Abstract

In this paper we study the twisted de Rham cohomology for an arrangement of hyperplanes. We prove formulas for basic constructions of arrangements: the twisted Künneth formula for products or decompositions, the long exact sequence for triple constructions, and the relation for coning and deconing constructions. Moreover, we obtain the vanishing, dimension, and basis of the twisted de Rham cohomology for an arrangement in general position and a generic arrangement with arbitrary weight.