Moduli spaces of sheaves on non-Kaehler Hermitian manifolds

非凯勒厄米流形上滑轮的模空间

• 批准号: 312567-2013
• 负责人: Moraru, Ruxandra
• 金额: $ 1.38万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=571773
• 关键词: Moduli; spaces; sheaves; non; Kaehler

The aim of this proposal is to study the geometric properties of moduli spaces of stable bundles and sheaves on compact complex manifolds that do not admit Kaehler metrics. An important problem in the study of complex manifolds is the classification of objects on these manifolds such as vector bundles and sheaves. Holomorphic vector bundles on polarized projective varieties have been extensively studied and their geometry is by now well understood; however, far less is known in the non-projective case. This is due to the fact that many of the techniques used for projective varieties only give partial results for general compact complex analytic manifolds. The goal of this research is to gain a better understanding of the non-projective picture by examining non-projective varieties such as non-Kaehler compact complex manifolds. Another motivation for the study of bundles on non-Kaehler complex manifolds comes from string theory. Of particular interest in this theory are complex manifolds with holomorphically trivial canonical bundles as they are potential backgrounds for compactifications of strings - certain vector bundles on the manifold determine these compactifications. Most of the models appearing in the physics literature have, until recently, been of strings compactified on elliptic Calabi-Yau manifolds equipped with a Kaehler metric. Nevertheless, there is now growing interest in non-Kaehler manifolds as other possible backgrounds for string compactifications. Some of the non-Kaehler complex manifolds considered in the proposal play a fundamental role in many areas of mathematics and physics. The results of this research will therefore provide many explicit examples of moduli spaces that will be of interest to a wide range of geometers, physicists, gauge theorists, researchers in the field of integrable systems, and model theorists.

本文的目的是研究不允许Kaehler度量的紧复流形上稳定束和束的模空间的几何性质。复杂流形研究中的一个重要问题是流形上物体的分类，如矢量束和矢量束。偏振射影变体上的全纯向量束已经得到了广泛的研究，它们的几何结构已经得到了很好的理解；然而，在非射影情况下，所知甚少。这是由于许多用于射影变的技术只能给出一般紧复解析流形的部分结果。本研究的目的是通过检验非射影变异体，如非kaehler紧复流形，来更好地理解非射影图像。