Mathematical Sciences: Complex Manifolds and Meromorphic Mappings

数学科学：复流形和亚纯映射

• 批准号: 9204037
• 负责人: Bernard Shiffman
• 金额: $ 10.5万
• 依托单位: Johns Hopkins University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-08-01 至 1995-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9204037&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Complex; Manifolds; Meromorphic

This project continues mathematical research into problems associated with the geometry of several complex variables and mappings defined on regions within such spaces. The work focuses on complex varieties, meromorphic mappings and holomorphic vector bundles. Work on meromorphic mappings seeks generalizations of Hartogs' theorems on separate analyticity and on holomorphic extendibility. Also to be investigated are Hartogs-type results for analytic subvarieties with possible application to the characterization of holomorphic chains of codimension greater than unity. Studies of holomorphic vector bundles concerns singular hermitian metrics on numerically effective line bundles on projective-algebraic manifolds. A continuation of work on cohomology vanishing theorems and sectional curvatures of indecomposable Hermitian-Einstein vector bundles on complex projective space will be carried out. Finally, the geometry of affine algebraic varieties and degree bounds for the division problem for special polynomial ideals will be studied. Complex function theory encompasses the study of differentiable functions of a several complex variables and related classes of functions such as boundary values of holomorphic functions. The subject is highly geometric; many of the problems concern the properties of various sets and how they transform by mappings composed of holomorphic functions. Applications of the theory to potential theory and fluid dynamics is now standard in engineering circles.

该项目继续研究与此类空间内部定义的几个复杂变量和映射相关的问题。 这项工作着重于复杂的品种，杂型映射和全态矢量束。 关于Meromormorphic映射的工作寻求对Hartogs定理的概括，并在单独的分析性和全体形态扩展性方面进行了概括。 还需要研究的是分析亚变量的Hartogs-type结果，并可能应用于大于统一性的综合质链的塑形链的表征。 关于全态载体束的研究涉及关于射影 - 偏见歧管上有效的线条捆绑包的奇特语指标。 在复杂的射影空间上，将继续进行有关共同体学的工作消失的定理和不可分解的Hermitian-Einstein矢量束的截面曲率。 最后，将研究特殊多项式理想的分区问题的仿射代数品种的几何形状和程度界限。 复杂函数理论涵盖了几个复杂变量和相关函数类别（例如全态函数的边界值）的可区分函数的研究。该受试者是高度几何的；许多问题都涉及各种集合的属性以及它们如何通过由全体形态函数组成的映射进行转换。 该理论在潜在理论和流体动力学上的应用现在已成为工程界的标准。