16 citations · 19 across the 8 of their papers we have counts for
8 papers
Obstructions for codimension one multiple fibers of Lagrangian and Calabi--Yau fibrations
Yoon-Joo Kim, Keiji Oguiso, Evgeny Shinder
We prove that compact hyper-Kähler manifolds with a Lagrangian fibration over a projective space have no multiple fibers in codimension one. This has several consequences for the s…
Meromorphic Group Actions and the Support Theorem for Lagrangian Fibrations
Mark Andrea de Cataldo, Yoon-Joo Kim, Christian Schnell
We prove several new results about Lagrangian fibrations on holomorphic symplectic complex spaces, under the assumption that the total space is Kähler (but possibly non-compact or…
Multiplicity of codimension 1 fibers in Lagrangian fibrations
Yoon-Joo Kim
Let be a Lagrangian fibration of a compact hyper-Kähler manifold. We prove that every codimension fiber of has multiplicity .
Kodaira-type classification of singular fibers of some minimal abelian fibrations
Yoon-Joo Kim
Let be a minimal abelian fibration of relative dimension over a curve. We classify all possible singular fibers having -dimensional ``abelian variety par…
Isotrivial Lagrangian fibrations of compact hyper-Kähler manifolds
Yoon-Joo Kim, Radu Laza, Olivier Martin
This article initiates the study of isotrivial Lagrangian fibrations of compact hyper-Kähler manifolds. We present four foundational results that extend well-known facts about isot…
The dual Lagrangian fibration of known hyper-Kähler manifolds
Yoon-Joo Kim
Given a Lagrangian fibration of a compact hyper-Kähler manifold of , , or -type, we construct a nat…
A conjectural bound on the second Betti number for hyper-Kähler manifolds
Yoon-Joo Kim, Radu Laza
In previous work, we noted that the known cases of hyper-Kähler manifolds satisfy a natural condition on the LLV decomposition of the cohomology; informally, the Verbitsky componen…
The LLV decomposition of hyper-Kaehler cohomology
Mark Green, Yoon-Joo Kim, Radu Laza +1
Looijenga--Lunts and Verbitsky showed that the cohomology of a compact hyper-Kähler manifold admits a natural action by the Lie algebra , generaliz…