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Journal of the London Mathematical Society Advance Access published online on July 31, 2008
Journal of the London Mathematical Society, doi:10.1112/jlms/jdn050
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© 2008 London Mathematical Society

The canonical volume of 3-folds of general type with {chi}≤0

Jungkai A. Chen

Department of Mathematics
National Taiwan University
Taipei 106
Taiwan

Meng Chen

Institute of Mathematics
School of Mathematical Sciences
Fudan University
Shanghai 200433
People's Republic of China
mchen@fudan.edu.cn

We prove that the canonical volume K3≥1/30 for all 3-folds of general type with {chi}(O)≤0. This bound is sharp.

2000 Mathematics Subject Classification 14E05, 14J30.

The first author was partially supported by the Taida Institute for Mathematical Sciences, the National Center for Theoretical Sciences, Taipei Office, and the National Science Council of Taiwan. The second author was supported by the Program for New Century Excellent Talents in University (#NCET-05-0358), the National Outstanding Young Scientist Foundation (#10625103) and the NNSFC (#10731030).

Received October 20, 2007;
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