This book gives a comprehensive treatment of the singularities that appear in the minimal model program and in the moduli problem for varieties. The study... > Lire la suite
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This book gives a comprehensive treatment of the singularities that appear in the minimal model program and in the moduli problem for varieties. The study of these singularities and the development of Mori's program have been deeply intertwined. Early work on minimal models relied on detailed study of terminal and canonical singularities, but many later results on log terminal singularities were obtained as consequences of the minimal model program. Recent work on the abundance conjecture and on moduli of varieties of general type relies on subtle properties of log canonical singularities and conversely, the sharpest theorems about these singularities use newly developed special cases of the abundance problem. This book untangles these interwoven threads, presenting a selfcontained and complete theory of these singularities. including many previously unpublished results.
This series is devoted to thorough, yet reasonably concise, treatments of topics in any branch of mathematics. Typically, a Tract takes up a single thread in a wide subject, and follows its ramifications, thus throwing light on its various aspects. Tracts are expected to be rigorous, definitive and of lasting value to mathematicians working in the relevant disciplines. Exercises can be included to illustrate techniques, summarize past work and enhance the hook's value as a seminar text. All volumes are properly edited and typeset, and are published, initially at least, in hardback.