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Jingcao Wu

Publications and source records attributed to Jingcao Wu.

16 recordsLinked to original sources
arXiv2026

Conditional Uniformization of Kähler Surfaces

We prove that a complete noncompact Kähler surface with nonnegative Ricci and nonnegative quadratic orthogonal bisectional curvature is contractible, and hence homeomorphic to $\mathbb{R}^4$, if it is simply connected at infinity. Under positive bisectional curvature, this removes the contractibility assumption from the conditional uniformization theorem of Datar--Pingali--Seshadri: strong Steinness and simple connectivity at infinity suffice to identify the surface biholomorphically with $\mathbb{C}^2$. We also derive bounded-gradient strictly plurisubharmonic exhaustions and uniform holomorphic kernel estimates for complete $U(n)$-invariant Kähler metrics on $\mathbb{C}^n$ with nonnegative bisectional curvature.

math.DG↗
arXiv2026

Deformations of Kähler and Balanced Hyperbolicity

We study the deformation stability of Kähler and balanced hyperbolicity. Balanced hyperbolicity is not open in general: in every complex dimension $N\geq5$ we construct a one-parameter family with balanced hyperbolic central fibre and non-balanced nearby fibres. For positive results, we develop three complementary mechanisms. A finite-dimensional moving-intersection framework tracks $\widetilde d$-bounded de Rham classes through moving pure-type loci; its Aeppli and Dolbeault realizations yield continuation, transversality, and positivity criteria for balanced and Kähler hyperbolicity. A topological mechanism combines the graded-ideal property of hyperbolic cohomology with the hard Lefschetz theorem to obtain saturation and higher-power propagation results. Finally, on the universal cover, we reduce the passage from a bounded $(\partial+\bar\partial)$-potential to a bounded $d$-primitive to a single bounded top-row $\partial$-equation, and package the dependence on the potential into a canonical quotient obstruction. Together, these viewpoints yield a range of deformation stability results.

math.DG↗
arXiv2026

Finite Gram Scalarization and Further Properties of Multiplier Submodule Sheaves

Let $(E,h)$ be a singular Hermitian vector bundle on a complex manifold $X$, and let \[ \mathcal E(h)_x=\{F\in\mathcal O(E)_x:|F|_h^2\in L^1_{\mathrm{loc},x}\} \] be its multiplier submodule sheaf. We introduce a finite plurisubharmonic Gram scalarization condition under which the higher-rank integrability problem reduces to finitely many scalar multiplier ideals. This reduction yields coherence and strong openness without imposing a general positivity hypothesis. When the scalar weights and the varying weight have analytic singularities, it also gives a theory of module jumping numbers, including a simultaneous-residue criterion for actual jumps. Finally, we study the induced Skoda filtration: Artin--Rees yields eventual periodicity, Tor controls whether periodicity starts at the scalar threshold, and a direct-image quotient measures the obstruction to descent.

math.CV↗
arXiv2026

A relative Nadel-type vanishing theorem

Let $f:X\rightarrow Y$ be a Kähler fibration from a complex manifold $X$ to an analytic space $Y$. We show several relative Nadel-type vanishing theorems.

math.AG↗
arXiv2022

On the global generation of higher direct images of pluricanonical bundles

Given a fibration $f$ between two projective manifolds $X$ and $Y$, we discuss the effective generation of the higher direct images $R^{i}f_{\ast}(K^{m}_{X})$, where $K^{m}_{X}$ is the $m$-th tensor power of the canonical bundle of $X$. In particular, we answer two questions posed by Popa--Schnell in [PS14].

math.AG↗
arXiv2021

Nefness of the direct images of pluricanonical bundles

Given a fibration $f$ between two projective manifolds $X$ and $Y$, we provide a sufficient condition such that the direct images $f_{\ast}(K_{X/Y}\otimes L\otimes\mathscr{I}(f,\|L\|))$ is nef, where $L$ is a holomorphic line bundle with non-negative relative Iitaka dimension and $\mathscr{I}(f,\|L\|)$ is the relative asymptotic multiplier ideal sheaf.

math.AG↗
arXiv2020

On the modified ideal sheaf

It is a sequel to (Wu in arXiv:2003.05187). In that paper, we introduce a notion called modified ideal sheaf in order to make an asymptotic estimate for the order of the cohomology group. Here we continue to a general discussion about this notion. As an application, we study the direct images associated with a pseudo-effective line bundle.

math.AG↗
arXiv2020

An eigenvalue estimate for the $\bar{\partial}$-Laplacian associated to a nef line bundle

We study the $\bar{\partial}$-Laplacian on forms taking values in $L^{k}$, a high power of a nef line bundle on a compact complex manifold, and give an estimate of the number of the eigenforms whose corresponding eigenvalues smaller than or equal to $λ$. In particular, the $λ=0$ case gives an asymptotic estimate for the order of the corresponding cohomology groups. It helps to generalize the Grauert--Riemenschneider conjecture. At last, we discuss the $λ=0$ case on a pseudo-effective line bundle.

math.CV↗
arXiv2019

A Kollár-type vanishing theorem

Let $f:X\rightarrow Y$ be a smooth fibration between two complex manifolds $X$ and $Y$, and let $L$ be a pseudo-effective line bundle on $X$. We obtain a sufficient condition for $R^{q}f_{\ast}(K_{X/Y}\otimes L)$ to be reflexive and hence derive a Kollár-type vanishing theorem.

math.CV↗
arXiv2018

Symmetrization of plurisubharmonic functions on the Fano manifolds

Given a compact complex manifold $Y$ with a negative line bundle $L\rightarrow Y$, we study the Schwarz-type symmetrization on the total space of $L$. We prove that this symmetrization does not increase the Monge-Ampère energy for the fibrewise $S^{1}$-invariant plurisubharmonic functions in the "unit ball" under some assumptions. As an application we generalize the sharp Moser-Trudinger inequality on the unit ball.

math.CV↗