Canonical stability of 3-folds of general type with $p_g\geq 3$
Abstract
Description
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 $p_g\leq 1$.
Latex 14 pages, the final version, to appear in International Journal of Mathematics
Latex 14 pages, the final version, to appear in International Journal of Mathematics