Non-vanishing implies numerical dimension one abundance

2025/05/08 by Liu, Jihao, Xu, Zheng · 3 citations
#14E30 #32J27 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.05250

Abstract

We show that the non-vanishing conjecture implies the abundance conjecture when ν≤ 1. We also prove the abundance conjecture in dimension ≤ 5 when κ≥ 0 and ν≤ 1 unconditionally.

Cited by

• Pluripotential geometry on semi-positive effective divisors of numerical dimension one
• Non-algebraicity of non-abundant foliations and abundance for adjoint foliated structures
• Nonvanishing results for Kähler varieties

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