Статьи, опубликованные в английской версии журнала
On the Existence of Equivariant Kähler Models of Certain Compact Complex Spaces
Jin Hong Kim Department of Mathematics Education, Chosun University, Gwangju, Republic of Korea
Аннотация:
Let
$X$ be a compact complex space in Fujiki's class
$\mathcal{C}$. In this paper, we show that
$X$ admits a compact Kähler model
${\tilde X}$, that is, there exists a projective bimeromorphic map
$\sigma\colon\tilde{X}\to X$ from a compact Kähler manifold
$\tilde{X}$ such that the automorphism group
$\operatorname{Aut}(X)$ lifts holomorphically and uniquely to a subgroup of
$\operatorname{Aut}({\tilde X})$. As a consequence, we also give a few applications to the Jordan property, the finiteness of torsion groups, and arbitrary large finite abelian subgroups for compact complex spaces in Fujiki's class
${\mathcal C}$.
Ключевые слова:
automorphism group, compact complex space in Fujiki's class
${\mathcal C}$, Jordan constant, Jordan property, strongly Jordan property, equivariant Kähler model.
Поступило: 27.07.2023
Исправленный вариант: 30.01.2024
Язык публикации: английский