2021/11/08 by Haidong Liu, Liu, Haidong
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG
paper · pdf · doi:10.48550/arxiv.2111.04270
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 This paper will not be published unless the remaining case can be excluded; v3, we revised the proof of Theorem 3.3
openalex publication_date 2021/11/08 · openalex created_date 2021/11/22 · arxiv created 2021/12/23 · arxiv updated 2021/12/24 · openalex updated_date 2026/07/28
We show that if X is a projective hyperkähler fourfold and there exists a nonzero effective divisor D which is not of bi-elliptic type and contained in the boundary of the nef cone of X, then X contains a rational curve. This is a very special case of Oguiso's conjecture for projective hyperkähler fourfolds.