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July, 2009 Gluing construction of compact complex surfaces with trivial canonical bundle
Mamoru DOI
J. Math. Soc. Japan 61(3): 853-884 (July, 2009). DOI: 10.2969/jmsj/06130853

Abstract

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 H 1 ( X , O X ) 0 , in which cases the smoothability result of Friedman [Fr] is not applicable.

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Mamoru DOI. "Gluing construction of compact complex surfaces with trivial canonical bundle." J. Math. Soc. Japan 61 (3) 853 - 884, July, 2009. https://doi.org/10.2969/jmsj/06130853

Information

Published: July, 2009
First available in Project Euclid: 30 July 2009

zbMATH: 1178.32013
MathSciNet: MR2552917
Digital Object Identifier: 10.2969/jmsj/06130853

Subjects:
Primary: 58J37
Secondary: 14J28, 32J15, 53C56

Rights: Copyright © 2009 Mathematical Society of Japan

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Vol.61 • No. 3 • July, 2009
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