AI 中文总结
本研究证明了有限下级线性非退化全纯曲线的Nevanlinna亏量的1/3次幂和可和，解决了Nevanlinna理论的公开问题，推广了Weitsman与Krutin的结果，并将其拓展到射影簇上的除子情形。
AI 中文摘要
针对处于一般位置的可数超平面族$H_j\subset \mathbb{P}^m$（$j\in\mathbb{N}$），以及从$\mathbb{C}$到$\mathbb{P}^m$的线性非退化有限下级全纯曲线$f$，我们证明其Nevanlinna亏量$δ_f(H_j)$满足$\sum_{j=1}^{\infty}δ_f(H_j)^{1/3}<\infty$。这解决了Nevanlinna理论中长期存在的公开问题，推广了Weitsman著名的标量端点定理（即$m=1$的情形）以及Krutin针对指数严格大于$1/3$的相关结果。借助相同的一致有限族估计，我们还得到了射影簇上由次数一致有界的环境超曲面截出的除子的对应端点定理，前提是这些除子关于该簇处于一般位置，且曲线不包含在任何除子的支集内。
英文摘要
For a countable family of hyperplanes $H_j\subset \mathbb{P}^m$, $j\in\mathbb{N}$, in general position and a linearly nondegenerate holomorphic curve $f\colon \mathbb{C}\to \mathbb{P}^m$ of finite lower order, we prove that the Nevanlinna defects $δ_f(H_j)$ satisfy $$ \sum_{j=1}^{\infty}δ_f(H_j)^{1/3}<\infty. $$ This resolves a long-standing open problem in Nevanlinna theory and extends Weitsman's celebrated scalar endpoint theorem (the case $m=1$) as well as Krutin's results for exponents strictly greater than $1/3$. The same uniform finite-family estimate yields the corresponding endpoint theorem for divisors cut out on a projective variety by ambient hypersurfaces of uniformly bounded degree, assuming that the divisors are in general position with respect to the variety and that the curve is not contained in the support of any divisor.
