Higher-Dimensional Analogs of Stable Curves

稳定曲线的高维模拟

• 批准号: 0401795
• 负责人: Valery Alexeev
• 金额: $ 29.15万
• 依托单位: University of Georgia Research Foundation Inc
• 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 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0401795&HistoricalAwards=false
• 关键词: Higher; Dimensional; Analogs; Stable; Curves

DMS-0401795Valery AlexeevThe project builds on PI's work towards generalizations of stable n-pointed curves to higher dimensions: stable pairs of dimension two and stable pairs with group action: toric, abelian, semiabelian and reductive. He will investigate several new applications of stable pairs and their moduli, including toric Torelli map; characterization of non-regular periodic polyhedral tilings; toric degenerations of reductive varieties with applications to mirror symmetry.The main subject of algebraic geometry - the primary field of the investigator's work - is to describe solutions of polynomial equations that are of fundamental importance to mathematics and its applications to science and engineering. Stable curves, whose higher-dimensional generalizations the investigator will continue to study, have seen exciting applications in number theory and in string theory in physics.

DMS-0401795VALERY ALEXEEV该项目基于PI的工作，旨在将稳定的N点曲线泛化到更高的尺寸：稳定的对稳定的尺寸二和稳定的对与群体动作：toric，abelian，abelian，semiabelian，semiabelian and Reductive。他将研究稳定对及其模量的几个新应用，包括曲曲托雷利地图；非规范周期性多面体瓷砖的表征；还应用于镜像对称性的还原性品种的复曲率退化。代数几何学的主要主题 - 研究者工作的主要领域 - 描述对数学及其对科学和工程的应用至关重要的多项式方程解决方案的解决方案。稳定的曲线是研究者将继续研究的较高维度的概括，在数量理论和弦理论中都在物理学中看到了令人兴奋的应用。