Effective bounds for very ample line bundles

• 成果类型: Article
• 署名作者: Demailly, JP
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s002220050052
• 发表日期: 1996
• 页码: 243-261
• 关键词: positive scalar curvature; multiplier ideal sheaves; kahler-einstein metrics; algebraic-varieties; inequalities; extension; THEOREM; systems

摘要

Let L be an ample line bundle on a non singular projective n-fold X. It is first shown that 2K(X) + mL is very ample for m greater than or equal to 2 + ((3n+1)(n)). 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 m(0) = m(0)(L(n),L(n-1). K-X) of degree less than or equal to n3(n) in the arguments, such that mL is very ample for m greater than or equal to m(0). The refinement is obtained through a new sharp upper bound for the dualizing sheaves of algebraic varieties embedded in projective space.