arXiv subjects

Chenghao Qing

Publications and source records attributed to Chenghao Qing.

4 recordsLinked to original sources

arXiv2026

A remark on Bogomolov type vanishing theorem

Several vanishing theorems for pseudo-effective line bundles are presented. All related results in the present note can be derived from already known theorems, in particular from the Steenbrink vanishing theorem and Boucksom's generalization of Bogomolov's vanishing theorem. No originality or priority is claimed for these statements; they are listed here merely as conjugate forms of the Kawamata--Viehweg vanishing theorem, for convenience of reference and comparison with existing literature.

math.AG↗

arXiv2026

A logarithmic Bogomolov--Sommese vanishing theorem on compact Kähler manifolds

In this paper, we establish a logarithmic Bogomolov--Sommese vanishing theorem in terms of numerical dimension for pseudo-effective line bundles on compact Kähler manifolds. As an application, we obtain a rigidity result with vanishing second Chern class for logarithmic cotangent bundles by combining the vanishing theorem with a structure theorem of Iwai and Matsumura.

math.AG↗

arXiv2026

Vanishing theorems for pseudo-effective line bundles

In the present paper, we establish a general Kawamata-Viehweg-Kollár-Nadel type vanishing theorem for higher direct images in terms of numerical dimension for closed positive currents on compact Kähler manifolds, unifying a number of important vanishing theorems.

math.CV↗

arXiv2025

On compact Kähler manifolds with pseudo-effective tangent bundle

In this paper, we prove that a compact Kähler manifold $X$ with pseudo-effective (resp. singular positively curved) tangent bundle admits a smooth (resp. locally constant) rationally connected fibration $ϕ\colon X \to Y$ onto a finite étale quotient $Y$ of a compact complex torus. This result extends the structure theorem previously established for smooth projective varieties to compact Kähler manifolds.

math.AG↗