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Classification of Algebraic Varieties
Edited by: Carel Faber, Royal Institute of Technology, Stockholm, Sweden, Gerard van der Geer, University of Amsterdam, The Netherlands, and Eduard Looijenga, Utrecht University, The Netherlands
A publication of the European Mathematical Society.
cover
EMS Series of Congress Reports
2011; 346 pp; hardcover
Volume: 3
ISBN-10: 3-03719-007-8
ISBN-13: 978-3-03719-007-4
List Price: US$98
Member Price: US$78.40
Order Code: EMSSCR/3
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Fascinating and surprising developments are taking place in the classification of algebraic varieties. The work of Hacon and McKernan and many others is causing a wave of breakthroughs in the minimal model program: we now know that for a smooth projective variety the canonical ring is finitely generated. These new results and methods are reshaping the field.

Inspired by this exciting progress, the editors organized a meeting at Schiermonnikoog and invited leading experts to write papers about the recent developments. The result is the present volume, a lively testimony to the sudden advances that originate from these new ideas.

This volume will be of interest to a wide range of pure mathematicians, but will appeal especially to algebraic and analytic geometers.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Readership

Graduate students and research mathematicians interested in pure mathematics.

Table of Contents

  • D. Abramovich and B. Hassett -- Stable varieties with a twist
  • F. Ambro -- Basic properties of log canonical centers
  • I. Bauer and F. Catanese -- Burniat surfaces I: Fundamental groups of moduli of primary Burniat surfaces
  • C. Birkar and M. Păun -- Minimal models, flip and finite generation: A tribute to V. V. Shokurov and Y.-T. Siu
  • F. Campana -- Remarks on an example of K. Ueno
  • F. Campana -- Special orbifolds and birational classification: A survey
  • J. A. Chen -- Birational geometry of threefolds
  • C. Ciliberto, O. Dumitrescu, R. Miranda, and J. Roé -- Emptiness of homogeneous linear systems with ten general base points
  • A. Corti -- Finite generation of adjoiint rings after Lazić: An introduction
  • T. de Fernex, L. Ein, and M. Mustaţă -- Log canonical thresholds on varieties with bounded singularities
  • G. Farkas -- Brill-Noether geometry on moduli spaces of spin curves
  • K. Frantzen and T. Peternell -- On the bimeromorphic geometry of compact complex contact threefolds
  • O. Fujino -- Introduction to the theory of quasi-log varieties
  • O. Fujino -- On Kawamata's theorem
  • Y. Kawamata -- Remarks on the cone of divisors
  • Y. Prokhorov -- p-elementary subgroups of the Cremona group of rank 3
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