Some birationality criteria on 3-folds with p g > 1

We give some birationality criteria for φ _m (m = 4, 5, 6, 7) on general type 3-folds with p _g ? 2 by means of an intensive classification. In particular, we show that φ ₇ is not birational if and only if p _g (X) = 2 and X admits a genus 2 curve family of canonical degree 2/3. When the canonical volume is large, we also characterize the birationality of φ ₄, φ ₅ and φ ₆.