TY - CHAP

T1 - Variation of numerical dimension of singular hermitian line bundles

AU - Matsumura, Shin Ichi

N1 - Funding Information:
This paper has been written during author’s stay in Institut de Mathématiques de Jussieu-Paris Rive gauche (IMJ-PRG). The author would like to thank the members of IMJ-PRG for their hospitality. He is supported by the Grant-in-Aid for Young Scientists (A) ♯17H04821 from JSPS and the JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers.
Funding Information:
Acknowledgements This paper has been written during author’s stay in Institut de Mathématiques de Jussieu-Paris Rive gauche (IMJ-PRG). The author would like to thank the members of IMJ-PRG for their hospitality. He is supported by the Grant-in-Aid for Young Scientists (A) ♯17H04821 from JSPS and the JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers.

PY - 2018

Y1 - 2018

N2 - The purpose of this paper is to give two supplements for vanishing theorems: One is a relative version of the Kawamata-Viehweg-Nadel type vanishing theorem, which is obtained from an observation for the variation of the numerical dimension of singular hermitian line bundles. The other is an analytic injectivity theorem for log canonical pairs on surfaces, which can be seen as a partial answer for Fujino’s conjecture.

AB - The purpose of this paper is to give two supplements for vanishing theorems: One is a relative version of the Kawamata-Viehweg-Nadel type vanishing theorem, which is obtained from an observation for the variation of the numerical dimension of singular hermitian line bundles. The other is an analytic injectivity theorem for log canonical pairs on surfaces, which can be seen as a partial answer for Fujino’s conjecture.

KW - Injectivity theorem

KW - Log canonical singularities

KW - Multiplier ideal sheaves

KW - Numerical dimension

KW - Singular hermitian metrics

KW - Vanishing theorem

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U2 - 10.1007/978-981-13-1672-2_19

DO - 10.1007/978-981-13-1672-2_19

M3 - Chapter

AN - SCOPUS:85053085138

T3 - Springer Proceedings in Mathematics and Statistics

SP - 247

EP - 255

BT - Springer Proceedings in Mathematics and Statistics

PB - Springer New York LLC

ER -