1.

Record Nr.

UNINA9910788869303321

Autore

Kollár János

Titolo

Singularities of the minimal model program / / János Kollár, Princeton University ; with the collaboration of Sándor Kovács, University of Washington [[electronic resource]]

Pubbl/distr/stampa

Cambridge : , : Cambridge University Press, , 2013

ISBN

1-107-23846-3

1-107-31478-X

1-107-30923-9

1-107-30703-1

1-107-31258-2

1-107-30598-5

1-139-54789-5

1-299-40318-2

1-107-30194-7

Descrizione fisica

1 online resource (x, 370 pages) : digital, PDF file(s)

Collana

Cambridge tracts in mathematics ; ; 200

Classificazione

MAT038000

Disciplina

516.3/5

Soggetti

Singularities (Mathematics)

Algebraic spaces

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Preface -- Introduction -- Preliminaries -- Canonical and log canonical singularities -- Examples -- Adjunction and residues -- Semi-log-canonical pairs -- Du Bois property -- Log centers and depth -- Survey of further results and applications -- Finite equivalence relations -- Ancillary results.

Sommario/riassunto

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interwoven threads, presenting a self-contained and complete theory of these singularities, including many previously unpublished results.