Let V be a complex nonsingular projective 3-fold of general type. We prove
P12(V)>0 and P24(V)>1 (which answers an open problem of J. Kollar and
S. Mori). We also prove that the canonical volume has an universal lower bound
Vol(V)≥1/2660 and that the pluri-canonical map Φm is
birational onto its image for all m≥77. As an application of our method,
we prove Fletcher's conjecture on weighted hyper-surface 3-folds with terminal
quotient singularities. Another featured result is the optimal lower bound
Vol(V)≥1/420 among all those 3-folds V with χ(OV)≤1.Comment: (updated version on October 15, 2007) 55 pages, a couple of missing
P_2 terms in Section 5 added and slight rearrangements to the contex