Song-Yan Xie

collaborators

4 papers

math.AG2026

Elliptic complements of cubic hypersurfaces

Song-Yan Xie

Let $D \subset P^{n}$ , $n ⩾ 2$ , be an arbitrary cubic hypersurface, and let $D_{red}$ denote its reduced support. We prove that $P^{n} ∖ D$ is hol…

math.AG2026

A Symmetry Method for Key Vanishing Lemmas and Optimal $2$ -Jet Thresholds for Hyperbolicity

Tao Cui, Lei Hou, Jianjun Liu +1

This manuscript reports on an ongoing project. The finite full-column-rank computations underlying the Key Vanishing Lemmas isolated below are currently undergoing exact computer-a…

math.CV2026

Vanishing of Invariant 2-Jet Differentials and Improved Hyperbolicity Degree Bounds in Dimension Two

Lei Hou, Dinh Tuan Huynh, JoÃ«l Merker +2

This paper establishes new degree bounds for Kobayashi hyperbolicity in dimension two. Our main results are: -- A very generic surface in $P^{3}$ of degree at least $17$ is…

math.CV2026

A Second Main Theorem for Entire Curves Intersecting Three Conics

Lei Hou, Dinh Tuan Huynh, JoÃ«l Merker +2

We establish a Second Main Theorem for entire holomorphic curves $ f: \mathbb{C} \to \mathbb{P}^2 $ intersecting a generic configuration of three conics \(\mathcal{C}= \mathcal{C…

Elliptic complements of cubic hypersurfaces

A Symmetry Method for Key Vanishing Lemmas and Optimal 2-Jet Thresholds for Hyperbolicity

Vanishing of Invariant 2-Jet Differentials and Improved Hyperbolicity Degree Bounds in Dimension Two

A Second Main Theorem for Entire Curves Intersecting Three Conics

A Symmetry Method for Key Vanishing Lemmas and Optimal $2$ -Jet Thresholds for Hyperbolicity