Effective bounds for very ample line bundles

Let be an ample line bundle on a non singular projective -fold . It is first shown that is very ample for . The proof develops an original idea of Y.T. Siu and is based on a combination of the Riemann-Roch theorem together with an improved Noetherian induction technique for the Nadel multiplier ideal sheaves. In the second part, an effective version of the big Matsusaka theorem is obtained, refining an earlier version of Y.T. Siu: there is an explicit polynomial bound of degree in the arguments, such that is very ample for . The refinement is obtained through a new sharp upper bound for the dualizing sheaves of algebraic varieties embedded in projective space. Oblatum 30-I-1995 & 18-V-1995