Mathematical Sciences: "Complex Manifolds and Meromorphic Mappings"

数学科学：“复流形和亚纯映射”

• 批准号: 8701808
• 负责人: Bernard Shiffman
• 金额: $ 7.19万
• 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: 1987
• 资助国家: 美国
• 起止时间: 1987-06-01 至 1989-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701808&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Complex; Manifolds; Meromorphic

This project continues work on problems centering on functions of several complex variables. The research uses geometric measure theory in complex analysis to characterize holomorphic chains in terms of locally rectifiable currents. Work will also be done on Hartogs-type theorems concerned with almost-everywhere separately meromorphic functions. Investigations will be carried out on value distribution theory of functions of several complex variables. The second main theorem and defect relations for non-equidimensional meromorphic mappings into complex projective manifolds will also be treated. Work on cohomology vanishing results for holomorphic line bundles satisfying weak numerical positivity conditions on complex projective manifolds will be carried out. Efforts will be made to construct semi-positive metrics on these line bundles. This research will provide valuable tools for studies in mappings between hypersurfaces.

该项目继续围绕以下问题开展工作： 多个复变量的函数 研究采用 复分析中的几何测度理论 用局部可求长流表示的全纯链。 工作也将做Hartogs型定理有关 几乎处处可分离亚纯函数 将对价值分配进行调查 多复变函数论 第二 非等维的主要定理和亏损关系 到复射影流形的亚纯映射将 也要治疗。 全纯直线上同调消失结果的研究 上满足弱数值正性条件的丛 将进行复投影流形。 努力将 在这些线上构造半正度量 捆起来。 这项研究将为研究提供有价值的工具， 超曲面之间的映射