Basic remarks on Lagrangian submanifolds of Hyper-Kähler manifolds

关于 $\mathscr{C}^\infty$ 可定义等价的一个注记

A remark on $\mathscr{C}^\infty$ definable equivalence

本文证明在 o-minimal 结构中，若子流形 M 可定义，则与其 C∞ 微分同胚且同胚映射接近恒等的可定义子流形 N 必与 M 可定义微分同胚，该同胚由管状邻域构造。

关于全纯辛流形上的代数余切子流形

On algebraically coisotropic submanifolds of holomorphic symplectic manifolds

研究全纯辛射影流形中的代数余切子流形，证明在非单直纹情况下，经过有限平展覆盖后，该子流形与辛流形可分解为乘积形式，并给出阿贝尔簇情形的完全证明及半丰典范丛的部分结果。

Monotonic lagrangian tori of standard and non standard types in toric and pseudotoric manifolds

In recent papers, summarized in survey [1], we construct a number of examples of non standard lagrangian tori on compact toric varieties and as well on certain non toric varieties which admit pseudotoric structures. Using this pseudotoric technique we explain how non standard lagrangian tori of Chekanov type can be constructed and what is the topological difference between standard Liouville tori and the non standard ones. However we have not discussed the natural question about the periods of the constructed twist tori; in particular the monotonicity problem for the monotonic case was not stu…