4 papers
Positive holomorphic sectional curvature on rational surfaces
Shiyu Zhang
In 1975, Hitchin proved that any compact complex surface admitting a Kähler metric with positive holomorphic sectional curvature is rational. Conversely, he constructed su…
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, ther…
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 i…
The Miyaoka-Yau inequality for minimal Kähler klt spaces
Chuanjing Zhang, Shiyu Zhang, Xi Zhang
In this paper, we obtain the generalized Bogomolov inequality for reflexive Higgs sheaves defined on the regular locus of compact Kähler klt spaces. As an application, we establis…