TY - JOUR
T1 - A Nadel vanishing theorem via injectivity theorems
AU - Matsumura, Shin ichi
N1 - Funding Information:
The author wishes to express his gratitude Professor Dano Kim for kindly giving some remarks on Siu’s metrics to him. He would like to thank the referee for carefully reading the manuscript. He is supported by the Grant-in-Aid for Young Scientists (B) 25800051 from JSPS.
PY - 2014/8
Y1 - 2014/8
N2 - The purpose of this paper is to establish Nadel type vanishing theorems with multiplier ideal sheaves of singular metrics admitting an analytic Zariski decomposition (such as, metrics with minimal singularities and Siu's metrics). For this purpose, we generalize Kollár's injectivity theorem to an injectivity theorem for line bundles equipped with singular metrics, by making use of the theory of harmonic integrals. Moreover we give asymptotic cohomology vanishing theorems for high tensor powers of line bundles.
AB - The purpose of this paper is to establish Nadel type vanishing theorems with multiplier ideal sheaves of singular metrics admitting an analytic Zariski decomposition (such as, metrics with minimal singularities and Siu's metrics). For this purpose, we generalize Kollár's injectivity theorem to an injectivity theorem for line bundles equipped with singular metrics, by making use of the theory of harmonic integrals. Moreover we give asymptotic cohomology vanishing theorems for high tensor powers of line bundles.
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U2 - 10.1007/s00208-014-1018-6
DO - 10.1007/s00208-014-1018-6
M3 - Article
AN - SCOPUS:84904440735
VL - 359
SP - 785
EP - 802
JO - Mathematische Annalen
JF - Mathematische Annalen
SN - 0025-5831
IS - 3-4
ER -