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Singularities of the minimal model p...

Kollár, János.

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Singularities of the minimal model program /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Singularities of the minimal model program // János Kollár, Princeton University ; with the collaboration of Sándor Kovács, University of Washington.
Author:	Kollár, János.
other author:	Kovács, Sándor J.
Published:	Cambridge :Cambridge University Press, : 2013.,
Description:	x, 370 p. :ill ;24 cm.
Subject:	Algebraic spaces. -
Online resource:	http://www.loc.gov/catdir/enhancements/fy1311/2012043204-t.html
Online resource:	http://www.loc.gov/catdir/enhancements/fy1311/2012043204-b.html
Online resource:	http://assets.cambridge.org/97811070/35348/cover/9781107035348.jpg
Online resource:	http://www.loc.gov/catdir/enhancements/fy1311/2012043204-d.html
ISBN:	9781107035348 (hbk.) :

Singularities of the minimal model program /
Kollár, János.

Singularities of the minimal model program /János Kollár, Princeton University ; with the collaboration of Sándor Kovács, University of Washington. - Cambridge :Cambridge University Press,2013. - x, 370 p. :ill ;24 cm. - Cambridge trats in mathematics ;200.

Includes bibliographical references and index.

Introduction --

"In 1982 Shigefumi Mori outlined a plan - now called Mori’s program or the minimal model program - whose aim is to investigate geometric and cohomological questions on algebraic varieties by constructing a birational model especially suited to the study of the particular question at hand. The theory of minimal models of surfaces, developed by Castelnuovo and Enriques around 1900, is a special case of the 2-dimensional version of this plan. One reason that the higher dimensional theory took so long in coming is that, while the minimal model of a smooth surface is another smooth surface, a minimal model of a smooth higher dimensional variety is usually a singular variety. It took about a decade for algebraic geometers to understand the singularities that appear and their basic properties. Rather complete descriptions were developed in dimension 3 by Mori and Reid and some fundamental questions were solved in all dimensions"--

ISBN: 9781107035348 (hbk.) :US85.00

LCCN: 2012043204Subjects--Topical Terms:

705293
Algebraic spaces.

LC Class. No.: QA614.58 / .K685 2013

Dewey Class. No.: 516.3/5

Singularities of the minimal model program /
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050 0 0 $a QA614.58 $b .K685 2013
082 0 0 $a 516.3/5 $2 23
100 1 $a Kollár, János. $3 2010735
245 1 0 $a Singularities of the minimal model program / $c János Kollár, Princeton University ; with the collaboration of Sándor Kovács, University of Washington.
260 # $a Cambridge : $b Cambridge University Press, $c 2013.
300 $a x, 370 p. : $b ill ; $c 24 cm.
490 1 0 $a Cambridge trats in mathematics ; $v 200
504 $a Includes bibliographical references and index.
505 0 # $t Introduction -- $t Preliminaries -- $t Canonical and log canonical singularities -- $t Examples -- $t Adjunction and residues -- $t Semi-log-canonical pairs -- $t Du Bois property -- $t Log centers and depth -- $t Survey of further results and applications -- $t Finite equivalence relations -- $t Ancillary results
520 # $a "In 1982 Shigefumi Mori outlined a plan - now called Mori’s program or the minimal model program - whose aim is to investigate geometric and cohomological questions on algebraic varieties by constructing a birational model especially suited to the study of the particular question at hand. The theory of minimal models of surfaces, developed by Castelnuovo and Enriques around 1900, is a special case of the 2-dimensional version of this plan. One reason that the higher dimensional theory took so long in coming is that, while the minimal model of a smooth surface is another smooth surface, a minimal model of a smooth higher dimensional variety is usually a singular variety. It took about a decade for algebraic geometers to understand the singularities that appear and their basic properties. Rather complete descriptions were developed in dimension 3 by Mori and Reid and some fundamental questions were solved in all dimensions"-- $c Provided by publisher.
520 # $a "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"-- $c Provided by publisher.
650 # 0 $a Algebraic spaces. $3 705293
650 # 0 $a Singularities (Mathematics) $3 588970
700 1 # $a Kovács, Sándor J. $q (Sándor József) $3 2010736
856 4 1 $3 Table of contents only $u http://www.loc.gov/catdir/enhancements/fy1311/2012043204-t.html
856 4 2 $3 Contributor biographical information $u http://www.loc.gov/catdir/enhancements/fy1311/2012043204-b.html
856 4 2 $3 Cover image $u http://assets.cambridge.org/97811070/35348/cover/9781107035348.jpg
856 4 2 $3 Publisher description $u http://www.loc.gov/catdir/enhancements/fy1311/2012043204-d.html