Communications in Analysis and Geometry

Volume 26 (2018)

Number 2

Inequality for Gorenstein minimal 3-folds of general type

Pages: 347 – 359



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


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 $\omega_X$.


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

2010 Mathematics Subject Classification

14C20, 14J30

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

Received 13 April 2016