Cohomology of local systems (Q2707468)

This survey is intended to provide a background for the authors' paper [\textit{A. Libgober} and \textit{S. Yuzvinsky}, Compos. Math. 121, No. 3, 337-361 (2000; Zbl 0952.52020)]. The central theme is the cohomology of local systems on quasi-projective varieties, especially on the complements to algebraic curves and arrangements of lines in \(\mathbb P^2\). The paper contains some of the highlights of \textit{P. Deligne}'s theory [Equations différentielles à point singulier, Lecture Notes Math. 163, Springer, Berlin (1970; Zbl 0244.14004)] and several examples from the theory of Alexander invariants of plane algebraic curves, developed mostly by the first author in the series of his papers. An interesting class of examples formed by complements to hyperplane arrangements, where cohomology of local systems and characteristic varieties can be often explicitly computed, is considered. Tools for computations are given by combinatorial invariants of arrangements: the intersection lattice and its Orlik-Solomon algebra. Several problems indicating possible further development are also included.NEWLINENEWLINEFor the entire collection see [Zbl 0952.00034].