Relative critical exponents, non-vanishing and metrics with minimal singularities

• 成果类型: Article
• 署名作者: Paun, Mihai
• 署名单位: Universite de Lorraine
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-011-0333-8
• 发表日期: 2012
• 页码: 195-258
• 关键词: invariance; extension; plurigenera

摘要

In this article we establish a very general non-vanishing statement, as well as several properties of metrics with minimal singularities of adjoint bundles. Our arguments combine the proof of the classical non-vanishing theorem due to V. Shokurov, as well as many ideas from Y.-T. Siu's analytic proof of the finite generation of the canonical ring. An important tool is the notion of relative critical exponent of two closed positive currents with respect to a measure.