Projective manifolds with small pluridegrees

Abstract

Let ? be a very ample line bundle on a connected complex pro- jective manifold M of dimension n > 3. Except for a short list of degenerate pairs (M, ?), K(KM + (n - 2)C) = n and there exists a morphism 7r: M -- M expressing M as the blowup of a projective manifold M at a finite set B, with KCM := KM + (n - 2)L nef and big for the ample line bundle L := (7r*LC)**.