Mathematical Research Letters

Volume 24 (2017)

Number 2

On canonically polarized Gorenstein 3-folds satisfying the Noether equality

Pages: 271 – 297



Yifan Chen (School of Mathematics and Systems Science, Beijing University of Aeronautics and Astronautics, Beijing, China)

Yong Hu (School of Mathematical Sciences, Fudan University, Shanghai, China)


We study canonically polarized Gorenstein minimal 3-folds satisfying $K^3_X = \frac{4}{3} p_g (X) - \frac{10}{3}$ and $p_g (X) \geq 7$. We characterize their canonical maps, describe a structure theorem for such $3$-folds and completely classify the smooth ones. New examples of canonically polarized smooth $3$-folds with $K^3_X = \frac{4}{3} p_g (X) - \frac{10}{3}$ and $p_g (X) \geq 7$ are constructed. These examples are natural extensions of those constructed by M. Kobayashi.

Received 25 December 2014

Accepted 8 April 2016

Published 24 July 2017