Author

Zehao Sha

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Preprint Sep 2026

PSC K\"ahler cones of minimal K\"ahler surfaces and a birational obstruction

We characterize the positive scalar curvature K\"ahler cone of every minimal compact K\"ahler surface with Kodaira dimension $-\infty$. By the Enriques--Kodaira classification, every such surface is either $\mathbb{P}^2$ or a geometrically ruled surface $\mathbb{P}(E)\to\Sigma_g$, where $E$ is a rank-two holomorphic ve...

Ze-Hao Sha · 1 citation

Preprint Sep 2026

Uniruledness and the sign of total scalar curvature

For every integer $n\ge3$, we construct a smooth projective manifold $X$ of complex dimension $n$ whose canonical bundle is not pseudoeffective, or equivalently, which is uniruled, but every K\"ahler metric has negative total scalar curvature. In particular, $X$ admits no K\"ahler metric of positive scalar curvature, w...

Ze-Hao Sha, Jian Wang · 0 citations

Preprint Aug 2026

Scalar curvature on K\"ahler blow-ups and systolic inequalities

In this paper, we develop the weighted level set method for a K\"ahler manifold $(X^n,\omega)$ admitting an almost holomorphic map to a possibly singular base $Z$, which is not uniruled. As a key intermediate result, we prove that any blowup $\operatorname{Bl}_SX$ of $X$ along smooth submanifolds $S$ of $ \operatorname...

Ze-Hao Sha, Jian Wang · 0 citations