37 research outputs found
Explicit birational geometry of 3-folds of general type, I
Let be a complex nonsingular projective 3-fold of general type. We prove
and for some positive
integer . A direct consequence is the birationality of the
pluricanonical map for all . Besides, the canonical
volume has a universal lower bound .Comment: 29 pages, Ann Sci Ecole Norm Sup (to appear
Explicit birational geometry of threefolds of general type
Let be a complex nonsingular projective 3-fold of general type. We prove
and (which answers an open problem of J. Kollar and
S. Mori). We also prove that the canonical volume has an universal lower bound
and that the pluri-canonical map is
birational onto its image for all . 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
among all those 3-folds with .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