Geometric and Analytic Problems in Several Complex Variables

多个复杂变量的几何和解析问题

• 批准号: 0400880
• 负责人: Linda Rothschild
• 金额: $ 25.6万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0400880&HistoricalAwards=false
• 关键词: Geometric; Analytic; Problems; Several; Complex

ABSTRACT:Rothschild and BaouendiA basic geometric and analytic problem in several complex variables is to determine when two real manifolds in multidimensional complex space are equivalent under an analytic transformation. The principal investigators will continue their research on several aspects of this fundamental problem. In particular, they will focus on determining when it is possible to reduce the equivalence problem to the much simpler one of solving systems of polynomial equations. They will also study which mappings between such manifolds are determined by finitely many derivatives at a given point. They expect that this study will lead to the discovery of new geometric, analytic, and algebraic properties of these important geometric objects. The study of the geometry of real manifolds in complex spaces is central to the field of several complex variables and to other areas of science, including geometry, mathematical physics and engineering. Progress on the problems proposed will likely have impact on these areas as well.

摘要：Rothschild 和 Bauuendi 多复变量中的一个基本几何和解析问题是确定多维复空间中的两个实流形在解析变换下何时等价。主要研究人员将继续对这个基本问题的几个方面进行研究。特别是，他们将专注于确定何时可以将等价问题简化为更简单的多项式方程组求解问题。他们还将研究这些流形之间的哪些映射是由给定点的有限多个导数确定的。他们期望这项研究将导致发现这些重要几何对象的新几何、解析和代数性质。复杂空间中实流形几何的研究是多个复变量领域以及其他科学领域（包括几何、数学物理和工程学）的核心。所提出问题的进展也可能对这些领域产生影响。