Inequality for Gorenstein minimal 3-folds of general type

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

Full Text (PDF format)

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

Received 13 April 2016

Published 7 May 2018