Author

Jian Wang

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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