Rationally Connected Varieties

合理关联的品种

• 批准号: 0969495
• 负责人: Chenyang Xu
• 金额: $ 12万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2011-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0969495&HistoricalAwards=false
• 关键词: Rationally; Connected; Varieties

The main aim of this proposal is to investigate a few questions in birational geometry. The first parts intends to study rationally connected varieties, which are the simplest algebraic varieties from many points of view. For non-proper varieties, there are various definitions of rational connectedness.The proposer will study their relations. He will also continue his study on the arithmetic property of rationally connected varieties. The other parts focus on the boundedness type questions of varieties or pairs. Especially, when the pair is of log general type, the PI investigator is trying to establish the uniform properties of their volumes.Algebraic varieties are roughly speaking the figures described by the solutions of polynomials. Algebraic geometry is a subject which aims to classify all algebraic varieties. In the birational sense, algebraic varieties are built up by some specific types of varieties. Rationally connected varieties and general type varieties are such fundamental building blocks. To understand them will largely improve our understanding of all algebraic varieties.

该提案的主要目的是研究Birational几何学中的一些问题。第一部分旨在研究合理联系的品种，这是从许多角度来看最简单的代数品种。对于非传播品种，有理性的联系有各种各样的定义。建议者将研究其关系。他还将继续研究合理联系品种的算术性能。其他部分集中于品种或对的有界性类型问题。特别是，当这对是对数一般类型时，PI研究者正在尝试建立其体积的均匀性能。代数品种大致说出了由多项式解决方案所描述的数字。代数几何形状是一个旨在对所有代数品种进行分类的主题。从典范的意义上讲，代数品种由某些特定类型的品种建立。合理连接的品种和一般类型的品种是这样的基本构建块。了解它们将在很大程度上提高我们对所有代数品种的理解。