关于射影超凯勒四维簇上有理曲线的存在性
代数几何
2021-12-24 v3
摘要
我们证明：若 是射影超凯勒四维簇，且存在一个非零有效除子 ，其非双椭圆型且包含在 的 nef 锥边界中，则 包含一条有理曲线。这是 Oguiso 关于射影超凯勒四维簇猜想的一个非常特殊的情形。
引用
@article{arxiv.2111.04270,
title = {On the existence of rational curves on projective hyperk\"ahler fourfolds},
author = {Haidong Liu},
journal= {arXiv preprint arXiv:2111.04270},
year = {2021}
}
备注
v1, 10 pages, any comments are welcome; v2, the previous version is revised significantly because there is a (bi-elliptic) case missing in proof of the main theorem. This paper will not be published unless the remaining case can be excluded; v3, we revised the proof of Theorem 3.3