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Arrangements of Hyperplanes--Sapporo 2009
Edited by: Hiroaki Terao, Hokkaido University, Japan, and Sergey Yuzvinsky, University of Oregon, Eugene
A publication of the Mathematical Society of Japan.
Advanced Studies in Pure Mathematics
2012; 570 pp; hardcover
Volume: 62
ISBN-10: 4-931469-67-1
ISBN-13: 978-4-931469-67-9
List Price: US$104
Member Price: US$83.20
Order Code: ASPM/62
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This book is the proceedings of the conference on Arrangements of Hyperplanes, held in August 2009 as the 2nd Mathematical Society of Japan Seasonal Institute.

The modern study of arrangements of hyperplanes started in the early 1980s. Since the object of study is simple (just a finite set of hyperplanes), there are various mathematical approaches to arrangements including algebra, topology, combinatorics, singularities, integral systems, hypergeometric functions, and statistics. Since numerous world-renowned experts gave talks at the 2nd MSJ-SI, this book covers many pioneering approaches and new topics in the theory of arrangements as well as indispensable classical results.

The book is recommended to any researcher or graduate student interested in arrangements of hyerplanes.

Volumes in this series are freely available electronically 5 years post-publication.

Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS.


Graduate students and research mathematicians interested in arrangements of hyperplanes.

Table of Contents

  • K. Aomoto -- Hypersphere arrangement and imaginary cycles for hypergeometric integrals
  • G. Denham and M. Schulze -- Complexes, duality and Chern classes of logarithmic forms along hyperplane arrangements
  • A. Deza, H. Miyata, S. Moriyama, and F. Xie -- Hyperplane arrangements with large average diameter: A computational approach
  • D. C. Cohen, G. Denham, M. Falk, and A. Varchenko -- Vanishing products of one-forms and critical points of master functions
  • Y. Haraoka -- Middle convolution for completely integrable systems with logarithmic singularities along hyperplane arrangements
  • H. Kimura -- On a problem of arrangements related to the hypergeometric integrals of confluent type
  • T. Kohno -- Hyperplane arrangements, local system homology and iterated integrals
  • A. Libgober -- On combinatorial invariance of the cohomology of the Milnor fiber of arrangements and the Catalan equation over function fields
  • E. Looijenga -- The KZ system via polydifferentials
  • K. Mimachi -- Solutions for some families of Fuchsian differential equations free from accessory parameters in terms of the integral of Euler type
  • J. V. Pereira -- Resonance webs of hyperplane arrangements
  • F. Mori and M. Salvetti -- Discrete topological methods for subspace arrangements
  • H. Schenck -- Hyperplane arrangements: Computations and conjectures
  • A. I. Suciu -- Resonance varieties and Dwyer-Fried invariants
  • H. Kamiya, A. Takemura, and N. Tokushige -- Application of arrangement theory to unfolding models
  • D. Tamaki -- On the homology of configuration spaces associated to centers of mass
  • T. Terasoma -- Varieties of lines on Fermat hypersurfaces
  • E. Mukhin, V. Tarasov, and A. Varchenko -- Three sides of the geometric Langlands correspondence for \(gl_n\) Gaudin model and Bethe vector averaging maps
  • A. K. Singh and U. Walther -- A note on Bockstein homomorphisms in local cohomology
  • M. Yoshinaga -- Arrangements, multiderivations, and adjoint quotient map of type ADE
  • S. Yuzvinsky -- Resonance varieties of arrangement complements
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