论文标题
藤族班级的高度kähler模型
Equivariant Kähler model for Fujiki's class
论文作者
论文摘要
令$ x $为富吉基（Fujiki）类$ \ mathcal {c} $的紧凑型复杂歧管，即承认一个大$（1,1）$ - 类$ [α] $。考虑$ \ text {aut}（x）$ BIHOLOLOMORMORGIC自动形态和$ \ text {aut} _ {[α]}（x）$通过Realback Via撤回。我们表明，$ x $接受$ \ text {aut} _ {[α]}（x）$ - epivariantkähler型号：有一个bimeromormorphic holomorphic地图$ c $σ\ colon \ colon \ colon \ colon \ widetilde {x}} $ \ text {aut} _ {[α]}（x）$通过$σ$抬起荷马晶。 有几个应用程序。我们表明，$ \ text {aut} _ {[α]}（x）$是一个只有有限的组件的谎言组。这概括了Lieberman和Fujiki在Kähler案上的早期结果。我们还表明，$ \ text {aut}（x）$的每个扭转子组几乎都是abelian，如果是扭转组，则$ \ text {aut}（x）$都是有限的。
Let $X$ be a compact complex manifold in Fujiki's class $\mathcal{C}$, i.e., admitting a big $(1,1)$-class $[α]$. Consider $\text{Aut}(X)$ the group of biholomorphic automorphisms and $\text{Aut}_{[α]}(X)$ the subgroup of automorphisms preserving the class $[α]$ via pullback. We show that $X$ admits an $\text{Aut}_{[α]}(X)$-equivariant Kähler model: there is a bimeromorphic holomorphic map $σ\colon \widetilde{X}\to X$ from a Kähler manifold $\widetilde{X}$ such that $\text{Aut}_{[α]}(X)$ lifts holomorphically via $σ$. There are several applications. We show that $\text{Aut}_{[α]}(X)$ is a Lie group with only finitely many components. This generalizes an early result of Lieberman and Fujiki on the Kähler case. We also show that every torsion subgroup of $\text{Aut}(X)$ is almost abelian, and $\text{Aut}(X)$ is finite if it is a torsion group.
