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