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Inequalities of Noether type for 3-folds of general type

Meng Chen
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Abstract

If $X$ is a smooth complex projective 3-fold with ample canonical divisor $K$, then the inequality $K^3\ge {2/3}(2p_g-7)$ holds, where $p_g$ 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. (A noether type of inequality lies, by all means, on the other side of the Miyaoka-Yau inequality from the geographical point of view.)

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Meng Chen. 2003-09-16. Inequalities of Noether type for 3-folds of general type. https://arxiv.org/abs/math/0110012

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