Xiangsen Qin

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20242026

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math.AG2026

Dolbeault Cohomology Growth under Curvature Rank Bounds

Xiangsen Qin

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 vec…

math.AG2026

Failure of local extension of semipositive metrics in a smooth projective family

Xiangsen Qin

We construct a smooth projective family of rational surfaces and an effective line bundle on its total space that give a negative answer to Păun's metric-extension question. The re…

math.DG2026

Chern Holomorphic Sectional Curvature: Canonical Ampleness, Rigidity, and Flatness Counterexamples

Xiangsen Qin, Yuanhong Tian

Let $X$ be a compact Brody-hyperbolic complex manifold admitting a strictly positive real $(1, 1)$ -current $T$ with smooth $d T$ and $d d^{c} T \leq 0$ . We prove that the canonical bundle $…