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Song-Yan Xie

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Preprint Aug 2026

Elliptic complements of cubic hypersurfaces

Let $D\subset\mathbb{P}^n$, $n\geqslant2$, be an arbitrary cubic hypersurface, and let $D_{\mathrm{red}}$ denote its reduced support. We prove that $\mathbb{P}^n\setminus D$ is holomorphically elliptic, and hence Oka, unless $D_{\mathrm{red}}$ is the union of three distinct hyperplanes containing a common codimension-t...

Song-Yan Xie · 1 citation

Preprint Aug 2026

Sharp Summability of Nevanlinna Defects for Finite-Lower-Order Holomorphic Curves

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 $\delta_f(H_j)$ satisfy $$ \sum_{j=1}^{\infty}\delta_f(H_j)^{1/3}<\infty....

Yun Du, Song-Yan Xie · 0 citations