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'Kodaira dimension'
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| Title of object: |
Kodaira dimension |
| Canonical Name: |
KodairaDimension |
| Type: |
Definition |
| Created on: |
2006-09-01 15:08:51 |
| Modified on: |
2006-11-15 10:19:22 |
| Classification: |
msc:14E05 |
Revision comment (for changes between this and next version):
| Hmm, another instance of copying from Wikipedia, perhaps? |
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Content:
This entry makes no sense, and the owner has rejected a correction requesting that it be fixed.
Named after the Japanese mathematician Kunihiko Kodaira, the {\em Kodaira dimension} $K$ of a non-singular algebraic variety $V$ is $t - 1$, where $t$ is the transcendence degree of a graded ring $R$.
If $V$ is on the projective line and $R$ is in the zero ring, the Kodaira dimension is set as $−1$. But the Kodaira dimension is 0 if the curve $K$ is both elliptic and a trivial bundle, and all plurigenera are 1. |
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