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# Mathematical Research Letters

## Volume 24 (2017)

### Number 2

### On canonically polarized Gorenstein 3-folds satisfying the Noether equality

Pages: 271 – 297

DOI: https://dx.doi.org/10.4310/MRL.2017.v24.n2.a2

#### Authors

#### Abstract

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