Deformation limits of projective manifolds: Hodge numbers and strongly Gauduchon metrics

• 成果类型: Article
• 署名作者: Popovici, Dan
• 署名单位: Universite de Toulouse; Universite Toulouse III - Paul Sabatier
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-013-0449-0
• 发表日期: 2013
• 页码: 515-534
• 关键词: compact kahler manifold; morse inequalities; complex-manifolds; currents; SURFACES; THEOREM

摘要

This paper is intended to start a series of works aimed at proving that if in a (smooth) complex analytic family of compact complex manifolds all the fibres, except one, are supposed to be projective, then the remaining (limit) fibre must be Moishezon. A new method of attack, whose starting point originates in Demailly's work, is introduced. While we hope to be able to address the general case in the near future, two important special cases are established here: the one where the Hodge numbers h (0,1) of the fibres are supposed to be locally constant and the one where the limit fibre is assumed to be a strongly Gauduchon manifold. The latter is a rather weak metric assumption giving rise to a new, rather general, class of compact complex manifolds that we hereby introduce and whose relevance to this type of problems we underscore.