Zehao Sha

collaborators

6 papers

math.AG2026

Uniruledness and the sign of total scalar curvature

Zehao Sha, Jian Wang

For every integer $n \geq 3$ , we construct a smooth projective manifold $X$ of complex dimension $n$ whose canonical bundle is not pseudoeffective, or equivalently, which is uniruled,…

math.DG2026

Positive scalar curvature Kähler cones on compact complex surfaces

Zehao Sha

We determine the positive scalar curvature Kähler cone of every minimal compact Kähler surface of Kodaira dimension $- \infty$ . By the Enriques--Kodaira classification, every such s…

math.DG2026

Scalar curvature on Kähler blow-ups and systolic inequalities

Zehao Sha, Jian Wang

In this paper, we develop the weighted level set method for a Kähler manifold $(X^{n}, ω)$ admitting an almost holomorphic map to a possibly singular base $Z$ , which is not uniruled.…

math.DG2026

A Variational Characterization of Positive Scalar Curvature Kähler metrics

Zehao Sha

We introduce the prescribed scalar curvature measure equation on a compact Kähler manifold. For a Kähler class of positive total scalar curvature, we prove that the following are e…

math.DG2026

The 2-systole on compact Kähler surfaces with positive scalar curvature

Zehao Sha

We study the 2-systole on compact Kähler surfaces of positive scalar curvature. For any such surface $(X, ω)$ , we prove the sharp estimate $\min_X S(ω)\cdot\operatorname{sys}_2(ω)\l…

math.DG2025

A 2-systolic inequality on non-rational compact Kähler surfaces with positive scalar curvature

Zehao Sha

In this note, we prove a 2-systolic inequality on compact positive scalar curvature Kähler surfaces admitting a nonconstant holomorphic map to a positive-genus compact Riemann surf…