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: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635463
• 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.

本文的目的是研究紧致复流形上不允许Kaehler度量的稳定丛和层的模空间的几何性质。复流形研究中的一个重要问题是对这些流形上的对象进行分类，如向量丛和层。全纯向量丛的极化投射簇已被广泛研究，他们的几何是现在很好地理解，但在非投射的情况下，知之甚少。这是由于许多用于射影簇的技术只给出一般紧致复解析流形的部分结果。本研究的目的是通过研究非投射流形，如非Kaehler紧致复流形，来更好地理解非投射图像。研究非Kaehler复流形上的丛的另一个动机来自弦理论。在这个理论中特别有趣的是具有全纯平凡正则丛的复流形，因为它们是弦的紧化的潜在背景-流形上的某些向量丛决定了这些紧化。直到最近，物理学文献中出现的大多数模型都是在椭圆形卡-丘流形上紧化的弦，流形上配备了凯勒度量。尽管如此，现在人们对非Kaehler流形作为弦紧化的其他可能背景的兴趣越来越大，其中一些非Kaehler复流形在数学和物理的许多领域中起着重要的作用。因此，这项研究的结果将提供许多明确的例子，模空间，将感兴趣的范围广泛的几何学家，物理学家，规范理论家，研究人员在该领域的可积系统，和模型理论家。