TY - GEN
T1 - Injectivity theorems with multiplier ideal sheaves and their applications
AU - Matsumura, Shin Ichi
N1 - Funding Information:
The author obtained an opportunity of discussion on the injectivity theorem and extension problem when he attended the conference “The 10th Korean Conference in Several Complex Variables”. He is grateful to the organizers. He would also like to thank the referee for carefully reading the paper and for suggestions. He is partially supported by the Grant-in-Aid for Young Scientists (B) 25800051 from JSPS.
Publisher Copyright:
© Springer Japan 2015.
PY - 2015
Y1 - 2015
N2 - 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).
AB - 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).
KW - Abundance conjecture
KW - Extension theorems
KW - Injectivity theorems
KW - L-methods
KW - Multiplier ideal sheaves
KW - Singular metrics
KW - The theory of harmonic integrals
KW - Vanishing theorems
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U2 - 10.1007/978-4-431-55744-9_18
DO - 10.1007/978-4-431-55744-9_18
M3 - Conference contribution
AN - SCOPUS:84950977623
SN - 9784431557432
T3 - Springer Proceedings in Mathematics and Statistics
SP - 241
EP - 255
BT - Complex Analysis and Geometry - KSCV 2014
A2 - Byun, Jisoo
A2 - Bracci, Filippo
A2 - Gaussier, Hervé
A2 - Kim, Kang-Tae
A2 - Shcherbina, Nikolay
A2 - Hirachi, Kengo
PB - Springer New York LLC
T2 - 10th Korean Conference on Several Complex Variables, KSCV 2014
Y2 - 7 August 2014 through 11 August 2014
ER -