Inequalities of Noether type for 3-folds of general type
Abstract
Description
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.)
25 pages, the final version, to appear in "Journal of the Mathematical Society of Japan"
25 pages, the final version, to appear in "Journal of the Mathematical Society of Japan"