Junchao Shentu

activity

20142026

most citedOn the Simultaneously Generation of Jets of the Adjoint Bundles

2 citations · 6 across the 19 of their papers we have counts for

collaborators

19 papers

math.AG2026

Arakelov inequality for families of pairs

Junchao Shentu

We establish an Arakelov-type inequality for a morphism $f : (X, Δ) \to S$ , where $(X, Δ)$ is a simple normal crossing semi-log canonical pair and $S$ is a smooth projective var…

math.AG2025

Stratified Hyperbolicity of the moduli stack of stable minimal models, II: Big Picard Theorem and the stratified Brody hyperbolicity

Junchao Shentu

This is the second paper on the global geometry of Birkar's moduli of stable minimal models (e.g., the KSBA moduli stack). We introduces a birationally admissible stratification of…

math.AG2025

Stratified Hyperbolicity of the moduli stack of stable minimal models, I

Junchao Shentu

In this paper, we introduce a birationally admissible stratification on the Deligne-Mumford stack of stable minimal models (e.g., the KSBA moduli stack), such that the universal fa…

math.AG2024

Kollár's package for polystable locally abelian parabolic Higgs bundles

Junchao Shentu, Chen Zhao

We generalize Kollár's package (including torsion freeness, injectivity theorem, vanishing theorem and decomposition theorem) to polystable locally abelian parabolic Higgs bundles…

math.AG2023

Hyperbolicity of the base of an admissible family of log canonical stable minimal models

Junchao Shentu, Chen Zhao

We investigate the stratified hyperbolicity properties of Birkar's moduli stack of log canonical (lc) stable minimal models. The main technical result is a construction of Viehweg-…

math.AG2023

Arakelov Type Inequalities and Deformation Boundedness of polarized varieties

Junchao Shentu

We give two kinds of generalizations of Arakelov type inequalities for higher dimensional families. These results give higher dimensional generalizations (in both fibers and bases)…

math.AG2022

Kollár's Package for Twisted Saito's S-sheaves

Junchao Shentu, Chen Zhao

We generalize Kollár's conjecture (including torsion freeness, injectivity theorem, vanishing theorem and decomposition theorem) to Saito's $S$ -sheaves twisted by a $Q$ -di…

math.AG2021★ 1 cited

$L^{2}$ -Extension of Adjoint bundles and Kollár's Conjecture

Junchao Shentu, Chen Zhao

We give a new proof of Kollár's conjecture on the pushforward of the dualizing sheaf twisted by a variation of Hodge structure. This conjecture was settled by M. Saito via mixed Ho…

math.AG2021

$L^{2}$ -Dolbeault resolution of the lowest Hodge piece of a Hodge module

Junchao Shentu, Chen Zhao

In this paper, we introduce a coherent subsheaf of Saito's $S$ -sheaf, which is a combination of the $S$ -sheaf and the multiplier ideal sheaf. We construct its $L^{2}$ -Dolbeault resol…

math.AG2021

$L^{2}$ -representation of Hodge Modules

Junchao Shentu, Chen Zhao

Over an arbitrary compact complex space or an arbitrary germ of complex space $X$ , we provide fine resolutions of pure Hodge modules with strict supports $I C_{X} (V)$ via dif…

math.CV2020

MacPherson's Conjecture via Hörmander Estimate

Junchao Shentu, Chen Zhao

In this notes we reprove MacPherson's conjecture on $L^{2} - (n, q)$ -cohomology through Demailly's formulation of Hörmander's Estimate. This approach allows us to weaken the condition o…

math.AG2019

On $E_{1}$ -degeneration for the special fiber of a semistable family

Mao Sheng, Junchao Shentu

We study the $E_{1}$ -degeneration of the logarithmic Hodge to de Rham spectral sequence of the special fiber of a semistable family over a discrete valuation ring. On the one hand, w…

math.AG2017★ 1 cited

Some examples of DR-indecomposable special fibers of semi-stable reductions over Witt rings

Mao Sheng, Junchao Shentu

We answer negatively an open problem of Illusie on the DR-decomposability of the log de Rham complex of the special fiber of a semi-stable reduction over the Witt ring. We also sho…

math.AG2017★ 2 cited

On the Simultaneously Generation of Jets of the Adjoint Bundles

Junchao Shentu, Yongming Zhang

In this paper, we investigate the problem of simultaneously generations of $r$ -jets of $ω_{X} \otimes L^{\otimes m}$ when $L$ is ample and base point free. It turns out that in this c…

math.AG2016

Smoothing of semistable Fano varieties

Junchao Shentu

Given any field $k$ (not necessarily perfect), we study the smoothing of a semistable Fano variety over $k$ . In characteristic 0, the reduced semistable Fano degenerate fibers of M…

math.NT2015

On the Integral Representation of Binary Quadratic Forms and the Artin Condition

Chang Lv, Junchao Shentu, Yingpu Deng

For diophantine equations of the form ax^2+bxy+cy^2+g=0 over Z whose coefficients satisfy some assumptions, we show that a condition with respect to Artin reciprocity map, which we…

math.NT2015★ 1 cited

On the Integral Representation of $a x^{2} + b y^{2}$ and the Artin Condition

Chang Lv, Junchao Shentu

Given a number field $F$ with $ø_{F}$ its ring of integers. For certain $a, b$ and $α$ in $ø_{F}$ , we show that the Artin condition is the only obstruction to the local-global principle…

math.AG2014

Strong Stability of Cotangent Bundles of Cyclic Covers

Lingguang Li, Junchao Shentu

Let $X$ be a smooth projective variety over an algebraically closed field $k$ of characteristic $p > 0$ of $dim X \geq 4$ and Picard number $ρ (X) = 1$ . Suppose that $X$ satisfies $H^i(…

math.AG2014★ 1 cited

Equivalence of two notions of log moduli stacks

Junchao Shentu

We show the equivalence between two notions of log moduli stacks which appear in literatures. In particular, we generalize M.Olsson's theorem of representation of log algebraic sta…

Arakelov inequality for families of pairs

Stratified Hyperbolicity of the moduli stack of stable minimal models, II: Big Picard Theorem and the stratified Brody hyperbolicity

Stratified Hyperbolicity of the moduli stack of stable minimal models, I

Kollár's package for polystable locally abelian parabolic Higgs bundles

Hyperbolicity of the base of an admissible family of log canonical stable minimal models

Arakelov Type Inequalities and Deformation Boundedness of polarized varieties

Kollár's Package for Twisted Saito's S-sheaves

L2-Extension of Adjoint bundles and Kollár's Conjecture

L2-Dolbeault resolution of the lowest Hodge piece of a Hodge module

L2-representation of Hodge Modules

MacPherson's Conjecture via Hörmander Estimate

On E1​-degeneration for the special fiber of a semistable family

Some examples of DR-indecomposable special fibers of semi-stable reductions over Witt rings

On the Simultaneously Generation of Jets of the Adjoint Bundles

Smoothing of semistable Fano varieties

On the Integral Representation of Binary Quadratic Forms and the Artin Condition

On the Integral Representation of ax2+by2 and the Artin Condition

Strong Stability of Cotangent Bundles of Cyclic Covers

Equivalence of two notions of log moduli stacks

$L^{2}$ -Extension of Adjoint bundles and Kollár's Conjecture

$L^{2}$ -Dolbeault resolution of the lowest Hodge piece of a Hodge module

$L^{2}$ -representation of Hodge Modules

On $E_{1}$ -degeneration for the special fiber of a semistable family

On the Integral Representation of $a x^{2} + b y^{2}$ and the Artin Condition