Mathematical Sciences: Line Bundle Convexity of Kahler Manifolds

数学科学：卡勒流形的线束凸性

• 批准号: 9102976
• 负责人: Karen Mortensen
• 金额: $ 4.01万
• 依托单位: University of Kentucky
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-15 至 1993-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9102976&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Line; Bundle; Convexity

This research will focus on function theoretic properties of L-convex manifolds. These L-convex manifolds are complex manifolds which are convex with respect to sections of a bundle L. L-convex manifolds have recently proven useful in attacking some classical problems in homomorphic convexity, such as the Levi problem and Shafarevich's Conjecture on the universal covering space of a projective variety. The project involves five areas of research: exhaustion functions, approximation of sections, embedding, cohomology with values in a coherent analytic sheaf, and characterization by local boundary conditions. This research is in the general area of the geometric analysis of surfaces or manifolds. These manifolds or surfaces exist in two, three, or many dimensions and involve both analytic and geometric techniques to understand and describe their structure. Often the surface is given coordinates and a metric which provides a measurement of distance or angle. In this project the manifolds have coordinates over the complex field and support a hermitian metric.

本文主要研究L-凸流形的函数论性质。这些L-凸流形是关于丛L的截面是凸的复流形。L-凸流形最近被证明在解决同态凸性中的一些经典问题时是有用的，例如射影簇的泛覆盖空间上的Levi问题和Shafarevich猜想。该项目涉及五个领域的研究：穷举函数，截面的逼近，嵌入，与相干解析束中的值的上同调，以及局部边界条件的刻画。这项研究是在曲面或流形的几何分析的一般领域。这些流形或曲面以二维、三维或许多维的形式存在，并涉及到了解和描述其结构的解析和几何技术。通常，表面被赋予坐标和提供距离或角度测量的度量值。在这个项目中，流形具有复数场上的坐标，并且支持厄米度规。