The Kuranishi-space of complex parallelisable nilmanifolds

言语理想与无阻碍的复平行可积 nilmanifolds

Verbal ideals and unobstructed complex parallelisable nilmanifolds

研究复平行可积 nilmanifolds 的变形是否受阻，证明其与 Lie 代数的现实条件及自由 Lie 代数的言语理想有关，指出维度 19 以下有限，20 维以上无限。

Deformation of 2-step Nilmanifolds with Abelian Complex Structures

We develop deformation theory for abelian invariant complex structures on a nilmanifold, and prove that in this case the invariance property is preserved by the Kuranishi process. A purely algebraic condition characterizes the deformations leading again to abelian structures, and we prove that such deformations are unobstructed. Various examples illustrate the resulting theory, and the behavior possible in 3 complex dimensions.

关于复结构与全纯向量丛对的形变分裂

On splittings of deformations of pairs of complex structures and holomorphic vector bundles

本文研究复流形与全纯向量丛对的Kuranishi空间分裂问题，证明Kähler情形和复可平行化nilmanifold平凡丛情形下可分解为直积，并给出非分裂的nilmanifold反例。

Stability of Abelian Complex Structures

Let $M = Γ\backslash G$ be a nilmanifold endowed with an invariant complex structure. We prove that Kuranishi deformations of abelian complex structures are all invariant complex structures, generalizing a result of C. Maclaughlin, H. Pedersen, Y.S. Poon and S. Salamon for 2-step nilmanifolds. We characterize small deformations that remain abelian. As an application, we observe that at real dimension six, the deformation process of abelian complex structures is stable within the class of nilpotent complex structures. We give an example to show that this property does not hold in higher dimensi…

Generalized deformations and holomorphic Poisson cohomology of solvmanifolds

We describe the generalized Kuranishi spaces of solvmanifolds with left-invariant complex structures. By using such description, we study the stability of left-invariantness of deformed generalized complex structures and smoothness of generalized Kuranishi spaces on certain classes of solvmanifolds. We also give explicit finite dimensional cohcain complexes which computes the holomorphic Poisson cohomology of nilmanifolds and solvmanifolds.