TY - JOUR
T1 - A Nadel vanishing theorem for metrics with minimal singularities on big line bundles
AU - Matsumura, Shin ichi
N1 - Funding Information:
The author wishes to express his deep gratitude to Professor Shigeharu Takayama who gave the main problem of this paper when he was a master's course student. He also would like to thank to the referee for helpful suggestions. He is supported by the Grant-in-Aid for Young Scientists (B) ♯ 25800051 from JSPS .
Publisher Copyright:
© 2015 Elsevier Inc.
PY - 2015/8/6
Y1 - 2015/8/6
N2 - The purpose of this paper is to establish a Nadel vanishing theorem for big line bundles 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 apply the theory of harmonic integrals and generalize Enoki's proof of Kollár's injectivity theorem. Moreover we investigate the asymptotic behavior of harmonic forms with respect to a family of regularized metrics.
AB - The purpose of this paper is to establish a Nadel vanishing theorem for big line bundles 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 apply the theory of harmonic integrals and generalize Enoki's proof of Kollár's injectivity theorem. Moreover we investigate the asymptotic behavior of harmonic forms with respect to a family of regularized metrics.
KW - Equation
KW - L<sup>2</sup>-Methods
KW - Multiplier ideal sheaves
KW - Singular metrics
KW - The theory of harmonic integrals
KW - Vanishing theorems
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U2 - 10.1016/j.aim.2015.03.019
DO - 10.1016/j.aim.2015.03.019
M3 - Article
AN - SCOPUS:84928814467
SN - 0001-8708
VL - 280
SP - 188
EP - 207
JO - Advances in Mathematics
JF - Advances in Mathematics
ER -