Degenerations and moduli

退化和模量

• 批准号: 0901309
• 负责人: Valery Alexeev
• 金额: $ 29.85万
• 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: 2009
• 资助国家: 美国
• 起止时间: 2009-06-01 至 2013-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0901309&HistoricalAwards=false
• 关键词: Degenerations; moduli

Valery Alexeev will continue his work on a wide variety of projects in algebraic geometry, many of them revolving around the construction and study of the moduli spaces of stable pairs and maps, the higher-dimensional generalizations of Deligne-Mumford-Knudson-Kontsevich's moduli spaces of stable curves and maps, as well as questions related to the Minimal Model Program, and to varieties with group action. The grant will contribute to training of graduate students and postdocs, and will support an active program in algebraic geometry at the University of Georgia.Algebraic geometry arose in the ancient times from the study of polynomial equations. It now employs a dazzling array of sophisticated tools and methods, and has connections and applications to most other fields of mathematics, as well as to physics and engineering. The study of moduli spaces is at the heart of algebraic geometry and answers questions such as: What is the totality of algebraic objects of a given type? Does it have a special structure? What happens to the objects when they "degenerate", for example when they are stretched to their physical limits?

瓦列里阿列克谢耶夫将继续他的工作在各种各样的项目在代数几何，其中许多围绕建设和研究的模空间的稳定对和地图，高维推广德利涅芒福德克努森Kontsevich的模空间的稳定曲线和地图，以及有关的问题最小模型计划，并与群体行动的品种。这笔赠款将用于培养研究生和博士后，并将支持格鲁吉亚大学的代数几何活动。代数几何起源于古代对多项式方程的研究。它现在采用了一系列令人眼花缭乱的复杂工具和方法，并与大多数其他数学领域以及物理学和工程学有联系和应用。模空间的研究是代数几何的核心，并回答了以下问题：给定类型的代数对象的总体是什么？它有特殊的结构吗？当物体“退化”时，例如当它们被拉伸到其物理极限时，会发生什么？