An effective Matsusaka big theorem
type: Item
instance of: scholarly article
title: An effective Matsusaka big theorem
zbMATH Open document ID: 0803.32017
author: Yum-Tong Siu
publication date: 1994-11-10T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75042
full work available at URL: urn-3:HUL.InstRepos:37960815
review text: We prove the following effective form of Matsusaka's Big Theorem. For an ample line bundle \(L\) over a compact complex manifold \(X\) of complex dimension \(n\) with canonical line bundle \(K_ X\), the line bundle \(mL\) is very ample for \(m\) no less than \[ (2^{3n-1} 5n)^{4^{n-1}} (3(3n- 2)^ nL^ n + K_ X \cdot L^{n - 1})^{4^{n - 1}3n} \over (6(3n - 2)^ n - 2n - 2)^{4^{n - 1} n - {2 \over 3}} (L^ n)^{4^{n-1} 3(n - 1)}. \]
Mathematics Subject Classification ID: 32J25
Mathematics Subject Classification ID: 14E25
Mathematics Subject Classification ID: 14C30
zbMATH DE Number: 683174
zbMATH Keywords: positive line bundle
zbMATH Keywords: holomorphic line bundle
zbMATH Keywords: compact complex manifold
zbMATH Keywords: estimates
zbMATH Keywords: closed positive current
zbMATH Keywords: Lelong number
zbMATH Keywords: strong Morse inequality
zbMATH Keywords: Matsusaka's big theorem
zbMATH Keywords: ample line bundle
MaRDI profile type: Publication
OpenAlex ID: W2167218575
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DOI: 10.5802/AIF.1378
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 683174