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A Nadel vanishing theorem via injectivity theorems

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Abstract

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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Acknowledgments

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) \(\sharp \)25800051 from JSPS.

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Correspondence to Shin-ichi Matsumura.

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Matsumura, Si. A Nadel vanishing theorem via injectivity theorems. Math. Ann. 359, 785–802 (2014). https://doi.org/10.1007/s00208-014-1018-6

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  • DOI: https://doi.org/10.1007/s00208-014-1018-6

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