Non-vanishing implies numerical dimension one abundance
Algebraic Geometry
2025-08-01 v2 Complex Variables
Differential Geometry
Abstract
We show that the non-vanishing conjecture implies the abundance conjecture when . We also prove the abundance conjecture in dimension when and unconditionally.
Cite
@article{arxiv.2505.05250,
title = {Non-vanishing implies numerical dimension one abundance},
author = {Jihao Liu and Zheng Xu},
journal= {arXiv preprint arXiv:2505.05250},
year = {2025}
}
Comments
24 pages. A part of the proof is refined by applying a result of Lazic-Peternell and now the log canonical case of Theorem 1.6 also holds