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arXiv · 2505.05250

Non-vanishing implies numerical dimension one abundance

Jihao Liu·Zheng Xu
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Abstract

We show that the non-vanishing conjecture implies the abundance conjecture when $\nu\leq 1$. We also prove the abundance conjecture in dimension $\leq 5$ when $\kappa\geq 0$ and $\nu\leq 1$ unconditionally.

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Jihao Liu, Zheng Xu. 2025-05-08. Non-vanishing implies numerical dimension one abundance. https://arxiv.org/abs/2505.05250

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