Moduli spaces of sheaves on non-Kaehler Hermitian manifolds

这一建议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。极化射影簇上的全纯向量丛已经得到了广泛的研究，它们的几何到目前为止已经被很好地理解了；然而，对于非射影情形，我们所知的要少得多。这是因为许多用于射影簇的技巧只给出了一般紧致复解析流形的部分结果。这项研究的目的是通过考察非射影变种，如非Kaehler紧致复流形，更好地理解非射影图景。

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.