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math.AG2026
Limits of Hyperkähler Manifolds and Moduli Spaces of Sheaves on K3 Surfaces
Kefeng Liu, Yang Shen
We prove that a compact strongly Gauduchon manifold which is a limit of compact hyperkähler manifolds is bimeromorphic to a compact hyperkähler manifold. This settles a case of a c…
math.AG2026
Sections of Hodge bundles II: Deformation of -classes and applications to Kähler geometry
Kefeng Liu, Yang Shen
Let be a compact Kähler manifold and its Kuranishi family, where may be singular and $\dim_{\C}B\ge1$. Using explicit sections of Hodge bundles, we…
math.AG2026
Sections of Hodge bundles I: Global theory and applications to period maps
Kefeng Liu, Yang Shen
We study global sections of Hodge bundles arising from two complementary constructions: a deformation-theoretic construction, which yields global geometric consequences for period…