Degenerations and Moduli in Algebraic Geometry

代数几何中的简并和模

• 批准号: 1603604
• 负责人: Valery Alexeev
• 金额: $ 24.9万
• 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: 2016
• 资助国家: 美国
• 起止时间: 2016-07-01 至 2020-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1603604&HistoricalAwards=false
• 关键词: Degenerations; Moduli; Algebraic; Geometry

This award supports research in algebraic geometry, a central branch of mathematics. It aims to understand, both practically and conceptually, solutions of systems of polynomial equations in many variables. Algebraic geometry has important applications to other fields of mathematics, such as number theory, topology, and analysis, as well as to physics, biology, cryptography, and engineering. The particular questions under study in this research project involve moduli spaces, which are sets that parameterize solutions of geometric classification problems. Some of the topics under study originated in string theory in physics, and results of this work may in turn find application there. Graduate students are involved in the project. The investigator will work on a range of questions in algebraic geometry centering on degenerations, compact moduli spaces of stable varieties and pairs, and connections to the minimal model program. A central project is the study of functorial compactifications of moduli spaces of K3 surfaces and their explicit combinatorial description. The investigator will also study the birational geometry of abelian six-folds.

该奖项支持数学中央分支代数几何学的研究。 它旨在在许多变量中实际和概念上了解多项式方程系统的解决方案。代数几何形状在其他数学领域（例如数字理论，拓扑和分析）以及物理，生物学，密码学和工程学都有重要的应用。该研究项目中研究的特定问题涉及模量空间，该空间是将几何分类问题解决方案参数化的集合。研究中的一些主题起源于物理学的弦理论，而这项工作的结果可能又可能在那里找到应用。研究生参与了该项目。研究者将在代数几何形状中进行一系列问题，以归化，紧凑的模量稳定品种和对的模量以及与最小模型程序的连接。一个中心项目是研究K3表面模量空间及其显式组合描述的功能压缩。研究者还将研究阿贝尔六倍的阿贝利亚人的生育几何形状。