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math.AG2026
Dolbeault Cohomology Growth under Curvature Rank Bounds
Xiangsen Qin
Let be a smooth Hermitian holomorphic line bundle on a compact complex manifold of dimension , and let 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…