A reduction of canonical stability index of 4 and 5 dimensional projective varieties with large volume

We study the canonical stability index of nonsingular projective varieties of general type with either large canonical volume or large geometric genus. As applications of a general extension theorem established in the first part, we prove some optimal results in dimensions 4 and 5, which are parallel to some well-known results on surfaces and 3-folds.Comment: Final version, 35 pages, Annales de l'Institut Fourier (to appear