Examples of a non-vanishing conjecture of Kawamata

Yu Lin Chang

doi:10.1142/S0129167X07004229

Examples of a non-vanishing conjecture of Kawamata

Yu Lin Chang^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Let M be a compact complex manifold with a positive holomorphic line bundle L, and K be its canonical line bundle. We give some sufficient conditions for the non-vanishing of H⁰ (M, K + L). We also show that the criterion can be applied to interesting classes of examples including all compact locally hermitian symmetric spaces of non-compact type, Mostow-Siu [10] surfaces, Kähler threefolds given by Deraux [3] and examples of Zheng [17].

Original language	English
Pages (from-to)	527-533
Number of pages	7
Journal	International Journal of Mathematics
Volume	18
Issue number	5
DOIs	https://doi.org/10.1142/S0129167X07004229
Publication status	Published - 2007 May
Externally published	Yes

Keywords

Adjoint line bundle
Kahler manifold
Kawamata
Non-positively curved
Non-vanishing

ASJC Scopus subject areas

General Mathematics

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10.1142/S0129167X07004229

Cite this

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title = "Examples of a non-vanishing conjecture of Kawamata",

abstract = "Let M be a compact complex manifold with a positive holomorphic line bundle L, and K be its canonical line bundle. We give some sufficient conditions for the non-vanishing of H0 (M, K + L). We also show that the criterion can be applied to interesting classes of examples including all compact locally hermitian symmetric spaces of non-compact type, Mostow-Siu [10] surfaces, K{\"a}hler threefolds given by Deraux [3] and examples of Zheng [17].",

keywords = "Adjoint line bundle, Kahler manifold, Kawamata, Non-positively curved, Non-vanishing",

author = "Chang, {Yu Lin}",

note = "Funding Information: I am indebted to my advisor Professor Sai-Kee Yeung for his constant encouragement and patience. I also appreciate the referee for the kindly suggestion which makes this paper more readable and complete. Especially the referee points out the two closely related papers Eyssidieux [4] and Takayama [12]. The author is totally supported by Purdue Research Foundation.",

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AU - Chang, Yu Lin

N1 - Funding Information: I am indebted to my advisor Professor Sai-Kee Yeung for his constant encouragement and patience. I also appreciate the referee for the kindly suggestion which makes this paper more readable and complete. Especially the referee points out the two closely related papers Eyssidieux [4] and Takayama [12]. The author is totally supported by Purdue Research Foundation.

PY - 2007/5

Y1 - 2007/5

N2 - Let M be a compact complex manifold with a positive holomorphic line bundle L, and K be its canonical line bundle. We give some sufficient conditions for the non-vanishing of H0 (M, K + L). We also show that the criterion can be applied to interesting classes of examples including all compact locally hermitian symmetric spaces of non-compact type, Mostow-Siu [10] surfaces, Kähler threefolds given by Deraux [3] and examples of Zheng [17].

AB - Let M be a compact complex manifold with a positive holomorphic line bundle L, and K be its canonical line bundle. We give some sufficient conditions for the non-vanishing of H0 (M, K + L). We also show that the criterion can be applied to interesting classes of examples including all compact locally hermitian symmetric spaces of non-compact type, Mostow-Siu [10] surfaces, Kähler threefolds given by Deraux [3] and examples of Zheng [17].

KW - Adjoint line bundle

KW - Kahler manifold

KW - Kawamata

KW - Non-positively curved

KW - Non-vanishing

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JF - International Journal of Mathematics

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Examples of a non-vanishing conjecture of Kawamata

Abstract

Keywords

ASJC Scopus subject areas

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