Lei Song

activity

20132026

most citedSingularities of secant varieties

2 citations · 5 across the 14 of their papers we have counts for

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13 papers · 1 filter

math.AG2026

The integral closedness of lattice simplices with large lattice length

Lei Song, Huanqi Wen, Zhixian Zhu

We prove that every $n$ -dimensional lattice simplex $P$ whose lattice length $L (P) \geq n - 1$ is integrally closed. As an application, we obtain a simple criterion for the projective…

math.AG2026

On Property $N_{p}$ of line bundles on smooth projective toric varieties

Lei Song, Huanqi Wen

We establish a criterion for Property $N_{p}$ for line bundles on a class of smooth projective toric varieties. More precisely, we prove that if a smooth projective toric variety $X$ …

math.AG2025

On the quantum cohomology of blow-ups of four-dimensional quadrics

Jianxun Hu, Huazhong Ke, Changzheng Li +1

We propose a conjecture relevant to Galkin's lower bound conjecture, and verify it for the blow-ups of a four-dimensional quadric at a point or along a projective plane. We also sh…

math.AG2021

On the image of Hitchin morphism for algebraic surfaces: The case $GL_{n}$

Lei Song, Hao Sun

The Hitchin morphism is a map from the moduli space of Higgs bundles $M_{X}$ to the Hitchin base $B_{X}$ , where $X$ is a smooth projective variety. When $X$ has dim…

math.AG2021

Curves contracted by the Gauss map

Lei Song

Given a singular projective variety in some projective space, we characterize the smooth curves contracted by the Gauss map in terms of normal bundles. As a consequence, we show th…

math.AG2018

Kodaira vanishing for singular varieties revisited

Donu Arapura, Lei Song

We correct the proof and slightly strengthen a Kodaira-type vanishing theorem for singular varieties originally due to Jaffe and the first author. Specifically, we show that if $L$ …

math.AG2018★ 1 cited

Regularity of structure sheaves of varieties with isolated singularities

Joaquín Moraga, Jinhyung Park, Lei Song

Let $X \subseteq P^{N}$ be a non-degenerate normal projective variety of codimension $e$ and degree $d$ with isolated $Q$ -Gorenstein singularities. We prove that the…

math.AG2018

On direct images of twisted pluricanonical sheaves on normal varieties

Chih-Chi Chou, Lei Song

We study the depth properties of certain direct image sheaves on normal varieties. Let $f : Y \to X$ be a proper morphism of relative dimension $d$ from a smooth variety onto…

math.AG2016

On the projective normality of cyclic coverings over a rational surface

Lei Song

Let $S$ be a rational surface with $dim ∣ - K_{S} ∣ \geq 1$ and let $π : X \to S$ be a ramified cyclic covering from a nonruled smooth surface $X$ . We show that for any integer $k\g…

math.AG2015

On the projective normality of double coverings over a rational surface

Biswajit Rajaguru, Lei Song

We study the projective normality of a minimal surface $X$ which is a ramified double covering over a rational surface $S$ with $dim ∣ - K_{S} ∣ \geq 1$ . In particular Horikawa surfaces,…

math.AG2015★ 2 cited

Singularities of secant varieties

Chih-Chi Chou, Lei Song

We study the singularities of the secant variety $Σ (X, L)$ associated to a smooth variety $X$ embedded by a sufficiently positive adjoint bundle $L$ . We show that $Σ (X, L)$ is always…

math.AG2014

On the universal family of Hilbert schemes of points on a surface

Lei Song

For a smooth quasi-projective surface $X$ and an integer $n \geq 3$ , we show that the universal family $Z^{n}$ over the Hilbert scheme $Hilb^{n} (X)$ of $n$ points has non $\math…

math.AG2013

On the singularities of effective loci of line bundles

Lei Song

We prove that every irreducible component of semi-regular loci of effective line bundles in the Picard scheme of a smooth projective variety has at worst rational singularities. Th…

The integral closedness of lattice simplices with large lattice length

On Property Np​ of line bundles on smooth projective toric varieties

On the quantum cohomology of blow-ups of four-dimensional quadrics

On the image of Hitchin morphism for algebraic surfaces: The case GLn​

Curves contracted by the Gauss map

Kodaira vanishing for singular varieties revisited

Regularity of structure sheaves of varieties with isolated singularities

On direct images of twisted pluricanonical sheaves on normal varieties

On the projective normality of cyclic coverings over a rational surface

On the projective normality of double coverings over a rational surface

Singularities of secant varieties

On the universal family of Hilbert schemes of points on a surface

On the singularities of effective loci of line bundles

On Property $N_{p}$ of line bundles on smooth projective toric varieties

On the image of Hitchin morphism for algebraic surfaces: The case $GL_{n}$