Jie Liu

activity

20162026

most citedCharacterization of projective spaces and

P^{r}

-bundles as ample divisors

7 citations · 29 across the 19 of their papers we have counts for

collaborators

19 papers

math.CA2026

Quantitative Fourier Restriction Estimates for Weyl Operators: Fourier-Support Dependence and Lower Bounds

Jie Liu

The Weyl calculus associates a function $a$ on phase space $R^{2 d}$ with the corresponding Weyl operator $L_{a}$ acting on $L^{2} (R^{d})$ . At $p = 2$ , this correspondence…

math.AG2023

Kawamata--Miyaoka type inequality for $Q$ -Fano varieties with canonical singularities

Haidong Liu, Jie Liu

Let $X$ be an $n$ -dimensional normal $Q$ -factorial projective variety with canonical singularities and Picard number one such that $X$ is smooth in codimension two, $- K_{X}$ …

math.RT2023

Dimension vectors of elementary modules of generalized Kronecker quivers

Jie Liu

Let $k$ be an algebraically closed field. The generalized or $n$ -Kronecker quiver $K (n)$ is the quiver with two vertices, called a source and a sink, and $n$ arrows from source to…

math.RT2022

Matrix Spherical Functions for $(SU (n + m), S (U (n) \times U (m)))$ : Two Specific Classes

Jie Liu

We consider the matrix spherical function related to the compact symmetric pair $(G, K) = (SU (n + m), S (U (n) \times U (m)))$ . The irreducible $K$ represe…

math.AG2022

Fano foliations with small algebraic ranks

Jie Liu

In this paper we study the algebraic ranks of foliations on $Q$ -factorial normal projective varieties. We start by establishing a Kobayashi-Ochiai's theorem for Fano folia…

math.AG2022★ 5 cited

On moment map and bigness of tangent bundles of $G$ -varieties

Jie Liu

Let $G$ be a connected algebraic group and let $X$ be a smooth projective $G$ -variety. In this paper, we prove a sufficient criterion to determine the bigness of the tangent bundle…

math.AG2021★ 5 cited

Algebraic fibre spaces with strictly nef relative anti-log canonical divisor

Jie Liu, Wenhao Ou, Juanyong Wang +2

Let $(X, Δ)$ be a projective klt pair, and $f : X \to Y$ a fibration to a smooth projective variety $Y$ with strictly nef relative anti-log canonical divisor $- (K_{X / Y} + Δ)$ . We prove t…

math.AG2021

Fano manifolds with big tangent bundle: a characterisation of $V_{5}$

Andreas Höring, Jie Liu

Let X be a Fano manifold with Picard number one such that the tangent bundle T_X is big. If X admits a rational curve with trivial normal bundle, we show that X is isomorphic to th…

math.CA2021★ 2 cited

$B C_{2}$ type multivariable matrix functions and matrix spherical functions

Erik Koelink, Jie Liu

Matrix spherical functions associated to the compact symmetric pair $(SU (m + 2), S (U (2) \times U (m))$ , having reduced root system of type $\mathrm{…

math.AG2020

Strictly nef vector bundles and characterizations of $P^{n}$

Jie Liu, Wenhao Ou, Xiaokui Yang

In this note, we give a brief exposition on the differences and similarities between strictly nef and ample vector bundles, with particular focus on the circle of problems surround…

math.AG2020★ 4 cited

Projective manifolds whose tangent bundle contains a strictly nef subsheaf

Jie Liu, Wenhao Ou, Xiaokui Yang

Suppose that $X$ is a projective manifold whose tangent bundle $T_{X}$ contains a locally free strictly nef subsheaf. We prove that $X$ is isomorphic to a projective bundle over a hy…

math.AG2020★ 2 cited

Examples of Fano manifolds with non-pseudoeffective tangent bundle

Andreas Höring, Jie Liu, Feng Shao

Let $X$ be a Fano manifold. While the properties of the anticanonical divisor $- K_{X}$ and its multiples have been studied by many authors, the positivity of the tangent bundle $T_{X}$ …

math.AG2019★ 2 cited

Fano manifolds containing a negative divisor isomorphic to a rational homogeneous space of Picard number one

Jie Liu

Let $X$ be an $n$ -dimensional complex Fano manifolds $(n \geq 3)$ . Assume that $X$ contains a divisor $A$ , which is isomorphic to a rational homogeneous space with Picard number one…

math.RT2019★ 1 cited

Odd singular vector formula for general linear Lie superalgebras

Jie Liu, Li Luo, Weiqiang Wang

We establish a closed formula for a singular vector of weight $λ - β$ in the Verma module of highest weight $λ$ for Lie superalgebra $gl (m ∣ n)$ when $λ$ is atypical with re…

math.AG2018

Note on quasi-polarized canonical Calabi-Yau threefolds

Jie Liu

Let $(X, L)$ be a quasi-polarized canonical Calabi-Yau threefold. In this note, we show that $∣ m L ∣$ is basepoint free for $m \geq 4$ . Moreover, if the morphism $Φ_{\vert 4L\…

math.AG2018

Seshadri constants of the anticanonical divisors of Fano manifolds with large index

Jie Liu

Seshadri constants, introduced by Demailly, measure the local positivity of a nef divisor at a point. In this paper, we compute the Seshadri constants of the anticanonical divisors…

math.AG2017

Stability of tangent bundles of complete intersections and effective restriction

Jie Liu

For $n \geq 3$ , let $M$ be an $(n + r)$ -dimensional irreducible Hermitian symmetric space of compact type and let $O_{M} (1)$ be the ample generator of $P i c (M)$ . Let $Y=H_1\cap…

math.AG2017★ 1 cited

Second Chern class of Fano manifolds and anti-canonical geometry

Jie Liu

Let $X$ be a Fano manifold of Picard number one. We establish a lower bound for the second Chern class of $X$ in terms of its index and degree. As an application, if $Y$ is a $n$ -d…

math.AG2016★ 7 cited

Characterization of projective spaces and $P^{r}$ -bundles as ample divisors

Jie Liu

Let $X$ be a projective manifold of dimension $n$ . Suppose that $T_{X}$ contains an ample subsheaf. We show that $X$ is isomorphic to $P^{n}$ . As an application, we derive the…

Quantitative Fourier Restriction Estimates for Weyl Operators: Fourier-Support Dependence and Lower Bounds

Kawamata--Miyaoka type inequality for Q-Fano varieties with canonical singularities

Dimension vectors of elementary modules of generalized Kronecker quivers

Matrix Spherical Functions for (SU(n+m),S(U(n)×U(m))): Two Specific Classes

Fano foliations with small algebraic ranks

On moment map and bigness of tangent bundles of G-varieties

Algebraic fibre spaces with strictly nef relative anti-log canonical divisor

Fano manifolds with big tangent bundle: a characterisation of V5​

BC2​ type multivariable matrix functions and matrix spherical functions

Strictly nef vector bundles and characterizations of Pn

Projective manifolds whose tangent bundle contains a strictly nef subsheaf

Examples of Fano manifolds with non-pseudoeffective tangent bundle

Fano manifolds containing a negative divisor isomorphic to a rational homogeneous space of Picard number one

Odd singular vector formula for general linear Lie superalgebras

Note on quasi-polarized canonical Calabi-Yau threefolds

Seshadri constants of the anticanonical divisors of Fano manifolds with large index

Stability of tangent bundles of complete intersections and effective restriction

Second Chern class of Fano manifolds and anti-canonical geometry

Characterization of projective spaces and Pr-bundles as ample divisors

Kawamata--Miyaoka type inequality for $Q$ -Fano varieties with canonical singularities

Matrix Spherical Functions for $(SU (n + m), S (U (n) \times U (m)))$ : Two Specific Classes

On moment map and bigness of tangent bundles of $G$ -varieties

Fano manifolds with big tangent bundle: a characterisation of $V_{5}$

$B C_{2}$ type multivariable matrix functions and matrix spherical functions

Strictly nef vector bundles and characterizations of $P^{n}$

Characterization of projective spaces and $P^{r}$ -bundles as ample divisors