Asian Journal of Mathematics

Volume 22 (2018)

Number 2

Special issue in honor of Ngaiming Mok (1 of 3)

Guest Editors: Jun-Muk Hwang, Korea Institute for Advanced Study; Yum-Tong Siu, Harvard University; Wing-Keung To, National University of Singapore; Stephen S.-T. Yau, Tsinghua University; Sai-Kee Yeung, Purdue University

On the canonical maps of nonsingular threefolds of general type

Pages: 299 – 306



Rong Du (Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, China)


Let $S$ be a nonsingular minimal complex projective surface of general type and the canonical map of $S$ is generically finite. Beauville showed that the geometric genus of the image of the canonical map is vanishing or equals the geometric genus of $S$ and discussed the canonical degrees for these two cases. We generalize his results to nonsingular minimal complex projective threefolds.


projective threefold, general type, canonical map, canonical degrees

2010 Mathematics Subject Classification

14E20, 14J30

The author’s research was sponsored by the National Natural Science Foundation of China (Grant No. 11471116, 11531007) and the Science and Technology Commission of Shanghai Municipality (Grant No. 18dz2271000).

Received 19 December 2016

Accepted 21 June 2017

Published 15 June 2018