AI 中文总结
针对光滑平面曲线补集的Green-Griffiths-Lang猜想，本文开发了计算负扭曲不变对数2-喷流微分族的有效方法，给出该猜想的计算准则并对若干曲线族验证，明确了相关例外轨迹。
AI 中文摘要
我们研究光滑平面曲线补集的Green-Griffiths-Lang猜想。我们开发了一种计算负扭曲不变对数2-喷流微分族的有效方法。通过将一阶对数喷流空间实现为$\boldsymbol{\text{P}}^2 \times \boldsymbol{\text{P}}^2$中的超曲面，我们将这些喷流微分编码为有限生成的双分次模，该模可显式计算。我们利用该描述给出Green-Griffiths-Lang猜想的计算准则，并对若干光滑平面曲线族验证了该准则。在具有足够多独立喷流微分的例子中，我们明确确定了例外轨迹。
英文摘要
We study the Green-Griffiths-Lang Conjecture for complements of smooth plane curves. We develop an effective method for computing a family of negatively twisted invariant logarithmic 2-jet differentials. By realizing the first logarithmic jet space as a hypersurface in $\mathbb{P}^2 \times \mathbb{P}^2$, we encode these jet differentials in a finitely generated bigraded module that can be computed explicitly. We use this description to give a computational criterion for the Green-Griffiths-Lang Conjecture and verify it for several families of smooth plane curves. In examples with sufficiently many independent jet differentials, we determine the exceptional locus explicitly.
CommentsAdded AI disclosure and corrected a few typos
