Moduli Spaces of Sheaves in Higher Dimensions

除了少数基本情况外，关于2维以上层的模空间的结构知之甚少。对于阿贝尔簇，我们有两个强大的技术：傅立叶-向井变换和Bridgeland稳定性条件。这些是相互联系的，我们可以在它们之间描述二维层的模空间。这个项目的目的是尝试在更高的维度上使用这些技术来探索模空间的结构。然后，我们可以用这个玩具模型来描述其他种类的层的模空间。

Little is known about the structure of the moduli spaces of sheaves above dimension 2 except for a few basiccases. For abelian varieties, we have two powerful techniques: the Fourier-Mukai transform and Bridgelandstability conditions. These are interlinked and between them we can describe the moduli spaces of sheaves indimension 2. The aim of this project is to attempt to use these techniques in higher dimensions to explore thestructure of the moduli spaces. We can then use this toy model to describe moduli spaces of sheaves on othervarieties.