Arrangements, Local Systems and Singularities

This volumecomprisesa setof lecturenotes fromthe CIMPASummer School, - rangements and Local systems and Singularities, held at Galatasaray University, Istanbul, during June11-22, 2007. Theschoolwasattendedby68mathematicians, 35 of them from 19 countries outside Turkey. The Summer School was made up of eleven short courses and ? ve seminars presented by an outstanding group of lecturers who covered a wide range of topics related to the concepts of arran- ments, localsystems andsingularities. Thelist of lectures ofthe workshopappears below. Mostmembers of the audienceweregraduatestudents oryoung researchers and the primary purpose of the school was to introduce them, in particular those from developing countries, to the many advances and opportunities in this widely applicable ? eld. Historically, researchonarrangementsofhyperplanes, starting with the work of V. I. A'rnold and E. Brieskorn and later Peter Orlik, was presented at meetings devoted mainly to discussions of singularities. Some of the articles in this volume demonstratethattheinteractionbetweenthesetwosubjectsis ongoingandpart- ularly productive. Beyond this, the volume is intended for a largeaudience in pure mathematics, including researchers and graduate students working in algebraic geometry, singularity theory, topology and related ? elds. The reader will ? nd in the ProblemSection at the end of the volumea variety of open problems proposed by the lecturers at the end of the School's sessions as directions ripe for further study and development.

Combinatorics of Covers of Complexified Hyperplane Arrangements.- Homological Aspects of Hyperplane Arrangements.- Pencils of Plane Curves and Characteristic Varieties.- Lectures on Orlik-Solomon Algebras.- Local Systems and Constructible Sheaves.- Geometry and Combinatorics of Resonant Weights.- The Characteristic Quasi-Polynomials of the Arrangements of Root Systems and Mid-Hyperplane Arrangements.- Toric Varieties and the Diagonal Property.- to Plane Curve Singularities. Toric Resolution Tower and Puiseux Pairs.- Surface Singularities Appeared in the Hyperbolic Schwarz Map for the Hypergeometric Equation.- On the Extendability of Free Multiarrangements.- Problem Session.