Generalized complex and Kähler geometry

广义复几何和凯勒几何

• 批准号: 355576-2008
• 负责人: Gualtieri, Marco
• 金额: $ 1.24万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2011
• 资助国家: 加拿大
• 起止时间: 2011-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=482761
• 关键词: Generalized; complex; hler; geometry

Generalized complex geometry is a unified approach to two separate fields: Symplectic geometry, used for classical mechanics, and Complex geometry, used for studying the behaviour of algebraic equations in arbitrary dimension. Besides unifying these two clasically separate disciplines, it also includes a family of intermediate geometries which are wholly new. These geometries turn out to provide alternative backgrounds for quantum field theories called "Flux compactifications", and hence are relevant to high-energy physics. The proposal has three related aims. First, to study the theoretical properties of these intermediate generalized complex structures, to form a more complete understanding of their intrinsic nature. Second, to pursue constructions of many examples of these intermediate geometrical structures. Lastly, to strengthen connections between generalized complex geometry and other fields of mathematics, such as Poisson geometry, geometry of 4-manifolds, and non-commutative geometry.

广义复杂的几何形状是对两个单独字段的统一方法：用于经典力学的符号几何形状和复杂的几何形状，用于研究任意维度中代数方程的行为。 除了统一这两个圆环分开的学科外，它还包括一个全新的中间几何形状家族。 这些几何形状可为量子场理论提供替代背景，称为“通量压缩”，因此与高能物理学有关。 该提案具有三个相关目标。首先，研究这些中间广义复合结构的理论特性，以更完整地了解它们的内在性质。第二，追求这些中间几何结构的许多例子的构造。 最后，为了加强广义复杂的几何形状与其他数学领域之间的联系，例如泊松几何，4个manifolds的几何形状和非交通性几何形状。