MARC Record from harvard_bibliographic_metadata

LEADER: 03591cam a2200421 i 4500
001 013661715-8
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008 121114t20132013enk b 001 0 eng
010 $a 2012043204
016 7 $a016191275$2Uk
020 $a9781107035348
020 $a1107035341
035 0 $aocn812251685
040 $aDLC$erda$beng$cDLC$dYDX$dBTCTA$dUKMGB$dOCLCO$dYDXCP$dCDX$dOCLCO
042 $apcc
050 00 $aQA614.58$b.K685 2013
082 00 $a516.3/5$223
084 $aMAT038000$2bisacsh
100 1 $aKollár, János.
245 10 $aSingularities of the minimal model program /$cJános Kollár, Princeton University ; with the collaboration of Sándor Kovács, University of Washington.
264 1 $aCambridge :$bCambridge University Press,$c2013, ©2013.
300 $ax, 370 pages ;$c24 cm.
336 $atext$2rdacontent
337 $aunmediated$2rdamedia
338 $avolume$2rdacarrier
490 1 $aCambridge tracts in mathematics ;$v200
520 $a"This book gives a comprehensive treatment of the singularities that appear in the minimal model program and in the moduli problem for varieties. The study of these singularities and the development of Mori's program have been deeply intertwined. Early work on minimal models relied on detailed study of terminal and canonical singularities but many later results on log terminal singularities were obtained as consequences of the minimal model program. Recent work on the abundance conjecture and on moduli of varieties of general type relies on subtle properties of log canonical singularities and conversely, the sharpest theorems about these singularities use newly developed special cases of the abundance problem. This book untangles these interwoven threads, presenting a self-contained and complete theory of these singularities, including many previously unpublished results"--$cProvided by publisher.
520 $a"In 1982 Shigefumi Mori outlined a plan - now called Mori's program or the minimal model program - whose aim is to investigate geometric and cohomological questions on algebraic varieties by constructing a birational model especially suited to the study of the particular question at hand. The theory of minimal models of surfaces, developed by Castelnuovo and Enriques around 1900, is a special case of the 2-dimensional version of this plan. One reason that the higher dimensional theory took so long in coming is that, while the minimal model of a smooth surface is another smooth surface, a minimal model of a smooth higher dimensional variety is usually a singular variety. It took about a decade for algebraic geometers to understand the singularities that appear and their basic properties. Rather complete descriptions were developed in dimension 3 by Mori and Reid and some fundamental questions were solved in all dimensions"--$cProvided by publisher.
504 $aIncludes bibliographical references and index.
505 0 $aPreface -- Introduction -- 1. Preliminaries -- 2. Canonical and log canonical singularities -- 3. Examples -- 4. Adjunction and residues -- 5. Semi-log canonical pairs -- 6. Du Bois property -- 7. Log centers and depth -- 8. Survey of further results and applications -- 9. Finite equivalence relations -- 10. Ancillary results -- References -- Index.
650 0 $aSingularities (Mathematics)
650 0 $aAlgebraic spaces.
650 7 $aMATHEMATICS / Topology.$2bisacsh
700 1 $aKovács, Sándor J.$q(Sándor József)
830 0 $aCambridge tracts in mathematics ;$v200.
988 $a20130417
049 $aHLSS
906 $0DLC