Some results on compact Kähler surfaces with non-positive bisectional curvature

Yu Lin Chang

doi:10.1007/s10711-009-9403-0

Some results on compact Kähler surfaces with non-positive bisectional curvature

Yu Lin Chang^*

^*Corresponding author for this work

Department of Mathematics

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

Abstract

In 1961 L. Frankel conjectured that any compact Kähler manifold of positive bisectional curvature is biholomorphic to a projective space. This was solved by S. Mori in 1979 and Siu and Yau in 1980. N. Mok in 1988 gave a full solution to the generalized Frankel's conjecture and proposed a dual problem. The results in this paper are attempts to give modified solutions to this problem in complex dimension two.

Original language	English
Pages (from-to)	65-70
Number of pages	6
Journal	Geometriae Dedicata
Volume	145
Issue number	1
DOIs	https://doi.org/10.1007/s10711-009-9403-0
Publication status	Published - 2010 Mar

Keywords

Frankel's conjecture
Kähler surfaces
Uniformization

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s10711-009-9403-0

Cite this

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abstract = "In 1961 L. Frankel conjectured that any compact K{\"a}hler manifold of positive bisectional curvature is biholomorphic to a projective space. This was solved by S. Mori in 1979 and Siu and Yau in 1980. N. Mok in 1988 gave a full solution to the generalized Frankel's conjecture and proposed a dual problem. The results in this paper are attempts to give modified solutions to this problem in complex dimension two.",

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AB - In 1961 L. Frankel conjectured that any compact Kähler manifold of positive bisectional curvature is biholomorphic to a projective space. This was solved by S. Mori in 1979 and Siu and Yau in 1980. N. Mok in 1988 gave a full solution to the generalized Frankel's conjecture and proposed a dual problem. The results in this paper are attempts to give modified solutions to this problem in complex dimension two.

KW - Frankel's conjecture

KW - Kähler surfaces

KW - Uniformization

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Some results on compact Kähler surfaces with non-positive bisectional curvature

Abstract

Keywords

ASJC Scopus subject areas

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