4 papers
Non-abelian Hodge correspondence over singular Kähler spaces
Chuanjing Zhang, Shiyu Zhang, Xi Zhang
In this paper, we establish the non-abelian Hodge correspondence over compact Kähler spaces with Kawamata log terminal (klt) singularities as well as over their regular loci, there…
Compact Kähler manifolds with partially semi-positive curvature
Shiyu Zhang, Xi Zhang
In this paper, we study MRC fibrations of compact Kähler manifolds with partially semi-positive curvature. We first prove that a compact Kähler manifold is rationally connected if…
The Miyaoka-Yau inequality for minimal Kähler klt spaces
Chuanjing Zhang, Shiyu Zhang, Xi Zhang
Let be a compact Kähler space with quotient singularities in codimension . In terms of orbifold Chern classes, we prove a generalized Bogomolov-Gieseker inequality for a ref…
On the structure of compact Kähler manifolds with nonnegative holomorphic sectional curvature
Shiyu Zhang, Xi Zhang
In this paper, we establish a "pseudo-effective" version of the holonomy principle for compact Kähler manifolds with nonnegative holomorphic sectional curvature. As applications, w…