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Kedlaya and J. Kim, Principal bundles and reciprocity laws in number theory B. Klingler, E. For example, there are surfaces of Kodaira dimension 1 for which the Iitaka fibration is an elliptic fibration over P 1. The minimal model and abundance conjectures would imply that every variety of Kodaira dimension 0 is birational to a Calabi-Yau variety with terminal singularities.
The Iitaka conjecture states that the Kodaira dimension of a fibration is at least the sum of the Kodaira dimension of the base and the Kodaira dimension of a general fiber; see Mori for a survey. The Iitaka conjecture helped to inspire the development of minimal model theory in the s and s.
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It is now known in many cases, and would follow in general from the minimal model and abundance conjectures. Nakamura and Ueno proved the following additivity formula for complex manifolds Ueno Although the base space is not required to be algebraic, the assumption that all the fibers are isomorphic is very special. Even with this assumption, the formula can fail when the fiber is not Moishezon. From Wikipedia, the free encyclopedia. Chen and M. Fujino and S. Mori, J. Theorems 5.
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Related Algebraic Geometry: Bowdoin, 1985, volume: 46 part 2 (Proceedings of Symposia in Pure Mathematics)
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