6 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 suc…
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…
Regularizing property of the twisted conical Kähler-Ricci flow
Jiawei Liu, Shiyu Zhang, Xi Zhang
In this paper, we show the regularity and uniqueness of the twisted conical Kähler-Ricci flow running from a positive closed current with zero Lelong number, which extends the regu…
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…