Peter Orlik

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. This book is the first comprehensive study of the subject. It treats arrangements with methods from combinatorics, algebra, algebraic geometry, topology, and group actions. It emphasizes general techniques which illuminate the connections among the different aspects of the subject. Its main purpose is to lay the foundations of the theory. Consequently, it is essentially self-contained and proofs are provided. Nevertheless, there are several new results here. In particular, many theorems that were previously known only for central arrangements are proved here for the first time in completegenerality. The text provides the advanced graduate student entry into a vital and active area of research. The working mathematician will findthe book useful as a source of basic results of the theory, open problems, and a comprehensive bibliography of the subject.

This book is based on two series of lectures given at a summer school on algebraic combinatorics at the Sophus Lie Centre in Nordfjordeid, Norway, in June 2003, one by Peter Orlik on hyperplane arrangements, and the other one by Volkmar Welker on free resolutions. Both topics are essential parts of current research in a variety of mathematical fields, and the present book makes these sophisticated tools available for graduate students.

Der Autor legt eine Methodenkritik wissenschaftlicher Menschenkenntnis vor, die einen Bruckenschlag zwischen Philosophie und Psychologie notig macht. Psychologen ubersehen allzuleicht, dass zwischenmenschliches Verstehen und Verstandenwerden begriffliche Fertigkeiten voraussetzt, die bestimmten (sprach-)logischen Kriterien genugen mussen. So liegt die Forderung nahe, dass der Psychodiagnostiker kunftig dem richtigen Gebrauch psychologischer Begriffe ebenso viel Sorgfalt zuwenden sollte, wie seit jeher der Beherrschung seines empirischen Handwerks. Worauf es dabei ankommt, lehrt die Auseinandersetzung mit der Sprachphilosophie Ludwig Wittgensteins und dessen Kritik an den in Alltag und Wissenschaft weit verbreiteten Fehldeutungen von Begriffen uber "Psychisches" (wie z.B. "Denken", "Unbewusstes", "Hoffnung", usw.). Diese, so seine Hauptthese, verdanken ihre Bedeutung nicht etwa, wie gerne behauptet wird, "inneren" Erlebnissen, sondern ihrer Verwendung in Sprachspielen innerhalb allgemein verbindlicher Lebensformen. Die psychologischen Konsequenzen dieser Position werden in diesem Buch, pro und contra, ausfuhrlich behandelt. Der thematische Bogen der siebzehn Kapitel ist weit gespannt. Er reicht von der Gegenuberstellung literarischer, handlungstheoretischer, philosophischer und biologischer Analysen des Spiel-Begriffs uber Wittgensteins Philosophie der Psychologie bis hin zur Frage nach den Legitimationskriterien "computergestutzter" Psychodiagnostik und mundet schliesslich in den Modellentwurf eines Verfahrens zur Analyse psychodiagnostischer Sprachspiele vom Typ der Selbstauskunft. Eine CD mit EDV-Programmen zur Erhebung und Auswertung von Selbstauskunften ist integraler Bestandteil des Buchs.

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. This book is the first comprehensive study of the subject. It treats arrangements with methods from combinatorics, algebra, algebraic geometry, topology, and group actions. It emphasizes general techniques which illuminate the connections among the different aspects of the subject. Its main purpose is to lay the foundations of the theory. Consequently, it is essentially self-contained and proofs are provided. Nevertheless, there are several new results here. In particular, many theorems that were previously known only for central arrangements are proved here for the first time in completegenerality. The text provides the advanced graduate student entry into a vital and active area of research. The working mathematician will findthe book useful as a source of basic results of the theory, open problems, and a comprehensive bibliography of the subject.