Nonexistence for complete Kähler–Einstein metrics on some noncompact manifolds

Peng Gao; Shing Tung Yau; Wubin Zhou

doi:10.1007/s00208-016-1486-y

Nonexistence for complete Kähler–Einstein metrics on some noncompact manifolds

Peng Gao, Shing Tung Yau, Wubin Zhou^*

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

Let M be a compact Kähler manifold and N be a subvariety with codimension greater than or equal to 2. We show that there are no complete Kähler–Einstein metrics on M- N. As an application, let E be an exceptional divisor of M. Then M- E cannot admit any complete Kähler–Einstein metric if blow-down of E is a complex variety with only canonical or terminal singularities. A similar result is shown for pairs.

Original language	English
Pages (from-to)	1271-1282
Number of pages	12
Journal	Mathematische Annalen
Volume	369
Issue number	3-4
DOIs	https://doi.org/10.1007/s00208-016-1486-y
Publication status	Published - 1 Dec 2017
Externally published	Yes

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Gao, P., Yau, S. T., & Zhou, W. (2017). Nonexistence for complete Kähler–Einstein metrics on some noncompact manifolds. Mathematische Annalen, 369(3-4), 1271-1282. https://doi.org/10.1007/s00208-016-1486-y

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abstract = "Let M be a compact K{\"a}hler manifold and N be a subvariety with codimension greater than or equal to 2. We show that there are no complete K{\"a}hler–Einstein metrics on M- N. As an application, let E be an exceptional divisor of M. Then M- E cannot admit any complete K{\"a}hler–Einstein metric if blow-down of E is a complex variety with only canonical or terminal singularities. A similar result is shown for pairs.",

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AB - Let M be a compact Kähler manifold and N be a subvariety with codimension greater than or equal to 2. We show that there are no complete Kähler–Einstein metrics on M- N. As an application, let E be an exceptional divisor of M. Then M- E cannot admit any complete Kähler–Einstein metric if blow-down of E is a complex variety with only canonical or terminal singularities. A similar result is shown for pairs.

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Nonexistence for complete Kähler–Einstein metrics on some noncompact manifolds

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