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.

广义复几何是两个独立领域的统一方法：用于经典力学的辛几何和用于研究任意维代数方程行为的复几何。 除了统一这两个经典上独立的学科，它还包括一个家庭的中间几何是全新的。 这些几何为量子场论提供了另一种背景，称为“通量紧致化”，因此与高能物理学有关。 该提案有三个相关的目标。首先，研究这些中间广义复结构的理论性质，形成对其内在本质的更完整的认识。第二，追求这些中间几何结构的许多例子的构造。 最后，加强广义复几何与其他数学领域的联系，如泊松几何、四维流形几何和非交换几何。