2 citations · 3 across the 9 of their papers we have counts for
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Dolbeault Type Cohomology Groups of Infinitesimal Deformations and Their Applications
Jiezhu Lin, Xuanming Ye
In this paper, we establish a kind of Dolbeault type cohomology groups for the purpose of studying the varying of complex structure invariants in infinitesimal deformations of any…
Decomposition, purity and fibrations by normal crossing divisors
Fouad El Zein, Dung Trang Lê, Xuanming Ye
We give a simple geometric proof of the decomposition theorem in terms of Thom-Whitney stratifications by reduction to fibrations by normal crossings divisors over the strata and e…
The jumping phenomenon of the dimensions of Bott-Chern cohomology groups and Aeppli cohomology groups
Jiezhu Lin, Xuanming Ye
Let be a compact complex manifold, and let be a small deformation of , the dimensions of the Bott-Chern cohomology groups $H_{\rm BC}^{p,q}(X(…
On the cohomology groups of local systems over Hilbert modular varieties via Higgs bundles
Stefan Müller-Stach, Mao Sheng, Xuanming Ye +1
Let be a Hilbert modular variety and a non-trivial local system over with infinite monodromy. In this paper we study Saito's mixed Hodge structure (MHS) on the…
Mixed Hodge complexes and L^2-cohomology for local systems on ball quotients
S. Müller-Stach, X. Ye, K. Zuo
We study the --cohomology of certain local systems on non-compact arithmetic ball quotients $X=Γ\backslash \B_n$, in particular vanishing and non--vanishing results. We also g…
The Jumping Phenomenon of the Dimensions of Cohomology Groups of Tangent Sheaf
Xuanming Ye
Let be a compact complex manifold, consider a small deformation of , the dimensions of the cohomology groups of tangent sheaf $H^q(X_t,\mathcal{T}_{X_…