Canonical stability of 3-folds of general type with $p_g\geq 3$
  We study the canonical stability of a smooth projective 3-fold $V$ of general type. We prove that   (1) $|5K_V|$ gives a birational map onto its image provided the geometric genus $p_g\geq 4$;   (2) $|6K_V|$ gives a birational map provided $p_g=3$.   Known examples show that both are optimal. This fact can be viewed as parallel to surface case, though people know very little on 3-folds of general type with $p_g\leq 1$. 
Meng Chen