Differential forms, uniformization and the Kodaira problem

微分形式、统一化和小平问题

• 批准号: 521356266
• 负责人: Dr. Patrick Graf
• 金额: --
• 依托单位: Lehrstuhl Mathematik I - Komplexe Analysis
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/521356266?language=en
• 关键词: Differential; forms; uniformization; Kodaira; problem

The project consists of three parts. The first part, "Uniformization", is about characterizing algebraic varieties (or, more generally, complex spaces) that admit certain symmetries via numerical conditions (e.g. intersection numbers). The second part, "Kodaira problem", studies the question which (non-algebraic) compact Kähler manifolds can be deformed to algebraic varieties. This would mean that algebraic methods can be used to study such Kähler manifolds. The third part, "Differential forms", will investigate under which circumstances differential forms on singular spaces can be extended to a resolution of singularities. Since this problem is already well-understood over the complex numbers, we will concentrate on base fields of positive characteristic.

该项目包括三个部分。第一部分，“一致化”，是关于通过数值条件（例如交集数）来表征允许某些对称性的代数簇（或者更一般地说，复空间）。第二部分“科代拉问题”，研究了（非代数的）紧致Kähler流形可变形为代数簇的问题。这意味着代数方法可以用来研究这样的凯勒流形。第三部分，“微分形式”，将研究在什么情况下，奇异空间上的微分形式可以扩展到奇异性的解决方案。由于这个问题在复数上已经很好理解了，我们将集中讨论具有正特征的基场。