4 papers
Invariant two-jets and effective hyperbolicity for complements of two plane curves
Lei Hou, Pengchao Wang, Song-Yan Xie
Let be a simple normal crossing union of smooth plane curves of degrees . We prove an effective Second Main Theorem for…
A Symmetry Method for Key Vanishing Lemmas and Optimal -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…
Vanishing of Invariant 2-Jet Differentials and Improved Hyperbolicity Degree Bounds in Dimension Two
Lei Hou, Dinh Tuan Huynh, Joël Merker +2
This paper establishes new degree bounds for Kobayashi hyperbolicity in dimension two. Our main results are: -- A very generic surface in of degree at least is…
A Second Main Theorem for Entire Curves Intersecting Three Conics
Lei Hou, Dinh Tuan Huynh, Joël 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…