Entire holomorphic curves into $\mathbb{P}^n(\mathbb{C})$ intersecting $n+1$ general hypersurfaces
Complex Variables
2023-11-30 v2 Algebraic Geometry
Abstract
Let be hypersurfaces in with total degrees , in general position and satisfying a generic geometric condition: every hypersurfaces intersect only at smooth points and the intersection is transversal. Then, for every algebraically nondegenerate entire holomorphic curve , we show a Second Main Theorem: in terms of defect inequality in Nevanlinna theory. This is the first result in the literature on Second Main Theorem for general hypersurfaces in with optimal total degrees.
Cite
@article{arxiv.2310.05433,
title = {Entire holomorphic curves into $\mathbb{P}^n(\mathbb{C})$ intersecting $n+1$ general hypersurfaces},
author = {Zhangchi Chen and Dinh Tuan Huynh and Ruiran Sun and Song-Yan Xie},
journal= {arXiv preprint arXiv:2310.05433},
year = {2023}
}
Comments
20 pages, 6 figures, comments are welcome