Singularities of the minimal model program / János Kollár, Princeton University ; with the collaboration of Sándor Kovács, University of Washington.

By:

Kollár, János [author.]

Contributor(s):

Series: Cambridge tracts in mathematics ; 200.Publisher: Cambridge : Cambridge University Press, 2013Description: 1 online resource (x, 370 pages) : digital, PDF file(s)Content type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9781139547895 (ebook)

Subject(s):

Genre/Form:

Electronic books.

Additional physical formats: Print version: : No titleDDC classification:

516.3/5 23

LOC classification:

QA614.58 .K685 2013

Online resources:

Click here to access online

Contents:

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.

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interwoven threads, presenting a self-contained and complete theory of these singularities, including many previously unpublished results.

Item type:

eBooks

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

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.