Toward a higher codimensional Ueda theory
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Ueda’s theory is a theory on a flatness criterion around a smooth hypersurface of a certain type of topologically trivial holomorphic line bundles. We propose a codimension two analogue of Ueda’s theory. As an application, we give a sufficient condition for the anti-canonical bundle of the blow-up of the three dimensional projective space at 8 points to be non semi-ample however admit a smooth Hermitian metric with semi-positive curvature.
KeywordsFlat line bundles Ueda’s theory The blow-up of the three dimensional projective space at eight points
Mathematics Subject Classification32J25 14C20
The author would like to give heartful thanks to his supervisor Prof. Shigeharu Takayama whose comments and suggestions were of inestimable value for my study. He also thanks Prof. Tetsuo Ueda and Prof. Yoshinori Gongyo for helpful comments and warm encouragements. He is supported by the Grant-in-Aid for Scientific Research (KAKENHI No. 25-2869) and the Grant-in-Aid for JSPS fellows. This work is supported by the Program for Leading Graduate Schools, MEXT, Japan.
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