Lingguang Li

activity

20102026

most citedOn a Conjecture of Lan-Sheng-Zuo on Semistable Higgs Bundles: Rank 3 Case

3 citations · 9 across the 16 of their papers we have counts for

collaborators

Showing math.AGShow all

14 papers · 1 filter

math.AG2026

The Birational Invariance Of Fundamental Group Schemes

Lingguang Li, Hao Wang

Let $k$ be a field, $f : X \to Y$ a birational morphism of integral connected schemes proper over $k$ with $Y$ normal, $x \in X (k)$ lying over $y \in Y (k)$ . For Tannakian cate…

math.AG2026

The Lefschetz Type Theorem For Fundamental Group Schemes

Lingguang Li, Niantao Tian

Let $k$ be a field, $X$ a connected scheme proper over $k$ , $D ⊊ X$ an ample effective connected divisor, $x \in D (k)$ . For Tannakian categories $C_{X}$ and $\mathca…

math.AG2026

Hecke curves in Frobenius strata of moduli space of rank 2 vector bundles

Lingguang Li, Hongyi Zhang

Let $k$ be an algebraically closed field with characteristic $2$ , and let $X$ be a smooth projective algebraic curve of genus $g ⩾ 2$ over $k$ . Let $\mathcal{M}^s_X(2,\math…

math.AG2026

The Künneth Formula Of Fundamental Group Schemes

Lingguang Li, Niantao Tian

Let $k$ be a field, $f : X \to S$ a proper morphism between connected schemes proper over $k$ , $x \in X (k)$ lying over $s \in S (k)$ , $X_{s}$ the fibre of $f$ over $s$ , $\mathcal{C…

math.AG2026

The Base Change Of Fundamental Group Schemes

Lingguang Li, Niantao Tian

Let $k$ be a field, $K / k$ a field extension, $X$ a connected scheme proper over $k$ , $x_{K} \in X_{K} (K)$ lying over $x \in X (k)$ , $C_{X}$ and $C_{X_{K}}$ the Tannakian c…

math.AG2020★ 1 cited

Irreducible cone spherical metrics and stable extensions of two line bundles

Lingguang Li, Jijian Song, Bin Xu

A cone spherical metric is called irreducible if any developing map of the metric does not have monodromy in $U (1)$ . By using the theory of indigenous bundles, we construct o…

math.AG2018★ 1 cited

Cone spherical metrics and stable vector bundles

Lingguang Li, Jijian Song, Bin Xu

Cone spherical metrics are conformal metrics with constant curvature one and finitely many conical singularities on compact Riemann surfaces. A cone spherical metric is called irre…

math.AG2018

Frobenius Stratification of Moduli Spaces of Vector Bundles in Positive characteristic. II

Lingguang Li

Let $X$ be a smooth projective curve of genus $g (X) \geq 1$ over an algebraically closed field $k$ of characteristic $p > 0$ , $\M^s_X(r,d)$ the moduli space of stable vector bundles o…

math.AG2017

Semistability of Rational Principal $G L_{n}$ -Bundles in Positive Characteristic

Lingguang Li

Let $k$ be an algebraically closed field of characteristic $p > 0$ , $X$ a smooth projective variety over $k$ with a fixed ample divisor $H$ . Let $E$ be a rational $G L_{n} (k)$ -bundle on…

math.AG2016★ 1 cited

Frobenius Stratification of Moduli Spaces of Rank $3$ Vector Bundles in Characteristic $3$ , I

Lingguang Li

Let $X$ be a smooth projective curve of genus $g \geq 2$ over an algebraically closed field $k$ of characteristic $p > 0$ , $F_{X} : X \to X$ the absolute Frobenius morphism. Let $\…

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.AG2013★ 3 cited

On a Conjecture of Lan-Sheng-Zuo on Semistable Higgs Bundles: Rank 3 Case

Lingguang Li

Let $X$ be a smooth projective curve of genus $g$ over an algebraically closed field $k$ of characteristic $p > 2$ . We prove that any rank $3$ nilpotent semistable Higgs bundle $(E,θ…

math.AG2011

The Morphism Induced by Frobenius Push-Forwards

Li Lingguang

Let $X$ be a smooth projective curve of genus $g (X) \geq 1$ over an algebraically closed field $k$ of characteristic $p > 0$ and $F_{X / k} : X \to X^{(1)}$ be the relative Frobeni…

math.AG2010

Instability of Truncated Symmetric Powers of sheaves

Lingguang Li, Fei Yu

Let $X$ be a smooth projective variety of dimension $n$ over an algebraically closed field $k$ of characteristic $p > 0$ . Let $F_{X} : X \to X$ be the absolute Frobenius morphism,…

The Birational Invariance Of Fundamental Group Schemes

The Lefschetz Type Theorem For Fundamental Group Schemes

Hecke curves in Frobenius strata of moduli space of rank 2 vector bundles

The Künneth Formula Of Fundamental Group Schemes

The Base Change Of Fundamental Group Schemes

Irreducible cone spherical metrics and stable extensions of two line bundles

Cone spherical metrics and stable vector bundles

Frobenius Stratification of Moduli Spaces of Vector Bundles in Positive characteristic. II

Semistability of Rational Principal GLn​-Bundles in Positive Characteristic

Frobenius Stratification of Moduli Spaces of Rank 3 Vector Bundles in Characteristic 3, I

Strong Stability of Cotangent Bundles of Cyclic Covers

On a Conjecture of Lan-Sheng-Zuo on Semistable Higgs Bundles: Rank 3 Case

The Morphism Induced by Frobenius Push-Forwards

Instability of Truncated Symmetric Powers of sheaves

Semistability of Rational Principal $G L_{n}$ -Bundles in Positive Characteristic

Frobenius Stratification of Moduli Spaces of Rank $3$ Vector Bundles in Characteristic $3$ , I