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Sheng Meng, Equivariant Kähler Model for Fujiki’s Class

May 31 @ 3:30 pm - 4:30 pm KST

B266, IBS Korea, Republic of


Sheng Meng
Let X be a compact complex manifold in Fujiki’s class C, i.e., admitting a big (1,1)-class [α]. Consider Aut(X) the group of biholomorphic automorphisms and Aut[α](X) the subgroup of automorphisms preserving the class [α] via pullback. We show that X admits an Aut[α](X)-equivariant Kähler model: there is a bimeromorphic holomorphic map σ : X~ → X from a Kähler manifold X~ such that Aut[α](X) lifts holomorphically via σ.
There are several applications. We show that Aut[α](X) is a Lie group with only finitely many components. This generalizes an early result of Fujiki and Lieberman on the Kähler case.We also show that every torsion subgroup of Aut(X) is almost abelian, and Aut(X) is finite if it is a torsion group.
This is a joint work with Jia Jia.


May 31
3:30 pm - 4:30 pm KST
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IBS Korea, Republic of


Yongnam Lee
IBS 복소기하학연구단 Center for Complex Geometry
기초과학연구원 복소기하학연구단
대전 유성구 엑스포로 55 (우) 34126
IBS Center for Complex Geometry
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
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