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On the complement of a hypersurface with flat normal bundle which corresponds to a semipositive line bundle


We investigate the complex analytic structure of the complement of a non-singular hypersurface with unitary flat normal bundle when the corresponding line bundle admits a Hermitian metric with semipositive curvature.

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The author would like to give heartfelt thanks to Professor Takeo Ohsawa for his comments and suggestions of inestimable value. He is also grateful to Professor Shin-ichi Matsumura for discussions on some results related to Theorem 1.1 (i). He also thanks the referee, whose comments made some of the statements and arguments clearer. This work was supported by JSPS Grant-in-Aid for Early-Career Scientists 20K14313, by MEXT Grant-in-Aid for Leading Initiative for Excellent Young ResearchersLEADER) No. J171000201, and partly by Osaka City University Advanced Mathematical Institute (MEXT Joint Usage/Research Center on Mathematics and Theoretical Physics).

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Correspondence to Takayuki Koike.

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Communicated by Ngaiming Mok.

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Koike, T. On the complement of a hypersurface with flat normal bundle which corresponds to a semipositive line bundle. Math. Ann. 383, 291–313 (2022).

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Mathematics Subject Classification

  • Primary 32J25
  • Secondary 14C20