Injectivity theorems with multiplier ideal sheaves and their applications

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10 Citations (Scopus)


The purpose of this survey is to present analytic versions of the injectivity theorem and their applications. The proof of our injectivity theorems is based on a combination of the L2-method for the (Formula presented)-equation and the theory of harmonic integrals. As applications, we obtain Nadel type vanishing theorems and extension theorems for pluri-canonical sections of log pairs. Moreover, we give some results on semi-ampleness related to the abundance conjecture in birational geometry (the minimal model program).

Original languageEnglish
Title of host publicationComplex Analysis and Geometry - KSCV 2014
EditorsJisoo Byun, Filippo Bracci, Hervé Gaussier, Kang-Tae Kim, Nikolay Shcherbina, Kengo Hirachi
PublisherSpringer New York LLC
Number of pages15
ISBN (Print)9784431557432
Publication statusPublished - 2015
Event10th Korean Conference on Several Complex Variables, KSCV 2014 - Gyeongju, Korea, Republic of
Duration: 2014 Aug 72014 Aug 11

Publication series

NameSpringer Proceedings in Mathematics and Statistics
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017


Conference10th Korean Conference on Several Complex Variables, KSCV 2014
Country/TerritoryKorea, Republic of


  • Abundance conjecture
  • Extension theorems
  • Injectivity theorems
  • L-methods
  • Multiplier ideal sheaves
  • Singular metrics
  • The theory of harmonic integrals
  • Vanishing theorems


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