If is a smooth complex projective 3-fold with ample canonical divisor , then the inequality holds, where denotes the geometric genus. This inequality is nearly sharp. We also give similar, but more complicated, inequalities for general minimal 3-folds of general type.
Meng CHEN. "Inequalities of Noether type for 3-folds of general type." J. Math. Soc. Japan 56 (4) 1131 - 1155, October, 2004. https://doi.org/10.2969/jmsj/1190905452