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# Communications in Analysis and Geometry

## Volume 26 (2018)

### Number 2

### Inequality for Gorenstein minimal 3-folds of general type

Pages: 347 – 359

DOI: https://dx.doi.org/10.4310/CAG.2018.v26.n2.a3

#### Author

#### Abstract

Let $X$ be a Gorenstein minimal 3-fold of general type. We prove the optimal inequality:\[K^3_X \geq \frac{4}{3} \chi (\omega_X) - 2 \; \textrm{,}\]where $\chi (\omega_X)$ is the Euler–Poincaré characteristic of the dualizing sheaf $\omega_X$.

#### Keywords

Albanese map, canonical map, 3-folds of general type

#### 2010 Mathematics Subject Classification

14C20, 14J30

The author is partially supported by the National Natural Science Foundation of China (Grant No. 11571076).

Received 13 April 2016

Published 7 May 2018