Degenerations and Moduli Spaces

退化和模空间

• 批准号: 2201222
• 负责人: Valery Alexeev
• 金额: $ 22.5万
• 依托单位: University of Georgia Research Foundation Inc
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2201222&HistoricalAwards=false
• 关键词: Degenerations; Moduli; Spaces

The award supports research in algebraic geometry, a central branch of mathematics which aims to understand, both practically and conceptually, solutions of systems of polynomial equations in many variables. The particular focus of this project is on the study of families of algebraic varieties and the way these varieties deform and break up. Such studies found important applications in other fields of mathematics, such as number theory and topology, as well as in string theory in physics. Graduate students will be involved in and supported by this project.The PI will work on a variety of projects centered around degenerations of algebraic varieties and functorial, geometrically meaningful compactifications of moduli spaces. The PI will continue his work on the geometrically meaningful compactifications of moduli spaces of lattice polarized K3 surfaces. He will also work on the intersection theory of KSBA moduli spaces.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该奖项支持代数几何的研究，这是数学的一个中心分支，旨在从实践和概念上理解多变量多项式方程组的解。这个项目的特别重点是研究代数簇的家庭和这些品种的变形和破裂的方式。这些研究在数学的其他领域，如数论和拓扑学，以及物理学中的弦理论中找到了重要的应用。研究生将参与并支持这个项目。PI将致力于围绕代数簇的退化和模空间的函子，几何意义的紧化的各种项目。PI将继续他的工作在几何意义上的紧化模空间的晶格极化K3表面。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。