Free actions of large groups on complex threefolds

Compact Kähler threefolds with the action of an abelian group of maximal rank

In this note, we study the normal compact Kähler (possibly singular) threefold $X$ admitting the action of a free abelian group $G$ of maximal rank, all the non-trivial elements of which are of positive entropy. If such $X$ is further assumed to have only terminal singularities, then we prove that it is either a rationally connected projective threefold or bimeromorphic to a quasi-étale quotient of a complex $3$-torus.

具有极大秩交换群作用的紧 Kähler 三维簇上等变极小模型纲领的存在性

Existence of the equivariant minimal model program for compact Kähler threefolds with the action of an abelian group of maximal rank

本文针对容许极大秩、正熵自由交换群作用的 $\mathbb{Q}$-factorial 紧 Kähler klt 三维簇，建立 $G$-等变对数极小模型纲领，并据此给出其有理连通或双纯等价于 $Q$-复环面的分类结论。

仿射二次三维簇的驯顺自同构的次数增长

Degree growth for tame automorphisms of an affine quadric threefold

本文利用赋值估计和方复形上的群作用，证明了保持仿射二次三维簇的驯顺自同构的动力次数避开 1 和 4/3 之间的值，并刻画了有限多个此类自同构随机乘积的次数增长指数为正的条件。