Gluing construction of compact complex surfaces with trivial canonical bundle

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概要

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• We obtain a new construction of compact complex surfaces with trivial canonical bundle. In our construction we glue together two compact complex surfaces with an anticanonical divisor under suitable conditions. Then we show that the resulting compact manifold admits a complex structure with trivial canonical bundle by solving an elliptic partial differential equation. We generalize this result to cases where we have other than two components to glue together. With this generalization, we construct examples of complex tori, Kodaira surfaces and K3 surfaces. Lastly we deal with the smoothing problem of a normal crossing complex surface X with at most double curves. We prove that we still have a family of smoothings of X in a weak sense even when X is not Kählerian or H1(X,OX)≠0, in which cases the smoothability result of Friedman [Fr] is not applicable.

• 社団法人 日本数学会の論文
• 2009-07-01

著者

• DOI Mamoru

  Department of Astronomy, School of Science, The University of Tokyo

• Doi Mamoru

  Department Of Mathematics Tokyo Institute Of Technology

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