Characterization of the 4-canonical birationality of algebraic 3-folds, II

Meng Chen, Qi Zhang

For nonsingular projective 3-folds $X$ (of general type) whose geometric genus $p_g=h^0(X,K_X)$ is $\ge 5$, the birationality of the fourth canonical map ${\phi }_{4,X}={\Phi }_{|4K_X|}$ was…