Moduli spaces for complex nilmanifolds

如果人们正在寻找一个奇异的复形或厄米特结构的可访问的例子，那么零流形已经被确立为流形的一个去到类。其主要特点是左不变结构的性质（通常）可以用李理论的方法来研究，即，幂零李代数上这类结构的分类已经引起了人们的广泛关注，但是在几何背景下所带来的额外困难却被大多数人所忽略。在这个项目中，我们的目标是分类同构类的左不变复结构的某些类的紧nilmanifold。我们想确定模空间作为复空间存在的情况，可能在固定额外的数据之后，并研究其性质。

Nilmanifolds have been established as one of the go-to classes of manifolds if one is looking for an accessible example of an exotic complex or hermitian structure. The main feature is that the properties of left-invariant structures (often) can be studied with methods from Lie theory, i.e., only depend on the corresponding Lie algebra.Classification of such structures on nilpotent Lie algebras has received a lot of attention, but the additional difficulties that arise in the geometric setting have mostly been neglected so far. In this project we aim to classify isomorphism classes of left-invariant complex structures for certain classes of compact nilmanifolds. We want to identify cases where the moduli space exists as a complex space, possibly after fixing additional data, and study its properties.