6 papers · 1 filter
Degenerations and Stability of Kähler Structures on Calabi--Yau Manifolds
Kefeng Liu, Yang Shen
In this paper, we study the degeneration and stability of Kähler structures on Calabi--Yau manifolds, namely compact Kähler manifolds with trivial canonical bundles, from the viewp…
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…
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…
Penrose transformation on flag domains
Kefeng Liu, Yang Shen
Building on our recent work, we construct the Penrose transformations of the cohomology groups of homogeneous line bundles on flag domains , where is of Hermit…
Vanishing Theorems and Complex Structures on Non-Classical Flag Domains
Kefeng Liu, Yang Shen
We prove that every nontrivial line bundle on a compact quotient of a non-classical flag domain has no nonzero global sections. The proof first establishes the Green--Griffiths--Ke…
Moduli spaces as ball quotients I, local theory
Kefeng Liu, Yang Shen
We give a Hodge theoretic criterion to characterize locally the period domains of certain projective manifolds to be complex balls.