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双有理几何中的几个问题。第一部分旨在研究有理连通簇，从许多角度来看，它们都是最简单的代数簇。对于非正当品种，理性关联性有多种定义。提出者将研究它们之间的关系。他还将继续研究有理关联簇的算术性质。其他部分侧重于簇或对的有界类型问题。特别是，当该对是对数一般类型时，PI研究者试图建立它们体积的一致性质。代数簇粗略地讲是由多项式的解描述的图形。代数几何是一门旨在对所有代数簇进行分类的学科。在双有理意义上，代数簇是由某些特定类型的簇建立起来的。合理连接品种和一般类型品种就是这样的基本构件。理解它们将在很大程度上提高我们对所有代数簇的理解。