Moduli spaces of sheaves

滑轮模空间

• 批准号: 312567-2008
• 负责人: Moraru, Ruxandra
• 金额: $ 0.87万
• 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: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=503604
• 关键词: Moduli; spaces; sheaves

In this proposal, the applicant intends to study moduli spaces of stable bundles and sheaves on non-Kaehler surfaces and threefolds. 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.

在这个提议中，申请人打算研究非Kaehler曲面和三重上的稳定丛和层的模空间。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的变种，如非Kaehler紧致复流形，来更好地理解非投射图像。