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Xiang-Sen Qin

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Preprint Oct 2026

Dolbeault Cohomology Growth under Curvature Rank Bounds

Let $L$ be a smooth Hermitian holomorphic line bundle on a compact complex manifold $X$ of dimension $n$, and let $r$ be its maximal curvature rank. For every fixed holomorphic vector bundle $E$, we prove $h^q(X,L^p\otimes E)=O_\varepsilon(p^{r+\varepsilon})$ for every $\varepsilon>0$ and every Dolbeault degree, with t...

Xiang-Sen Qin · 0 citations

Preprint Sep 2026

Constant Chern Holomorphic Sectional Curvature: Rigidity and Counterexamples to the Flatness Conjecture

We prove rigidity results for Hermitian metrics of constant Chern holomorphic sectional curvature and construct counterexamples to the flatness conjecture. On a compact complex manifold in Fujiki's class $\mathcal C$ of dimension $n\ge2$, every such metric with nonpositive curvature is K\"ahler; its universal cover is...

Xiang-Sen Qin, Yuan-Hong Tian · 2 citations