Compact Kähler manifolds with nef anti-canonical bundle

2025/06/29 by Shin‐ichi Matsumura, Juanyong Wang, Matsumura, Shin-ichi +5 · 3 citations
Mathematics · #14E30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Primary 32Q30 #Secondary 14C30

paper · pdf · doi:10.48550/arxiv.2506.23218

openalex publication_date 2025/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that a compact Kähler manifold X with the nef anti-canonical bundle -K_X admits a locally trivial fibration ϕ\colon X → Y, where the fiber F is a rationally connected manifold and the base Y is a Calabi--Yau manifold. We introduce a suitable approach that extends the strategy of Cao--Höring, originally developed for smooth projective varieties, to more general singular Kähler spaces. A key technical ingredient is a flatness criterion for pseudo-effective sheaves with vanishing first Chern class.

Citations

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Cited by

• Pluripotential geometry on semi-positive effective divisors of numerical dimension one
• Beauville-Bogomolov decomposition for klt varieties
• Variation of Kahler-Einstein metrics with mixed singularities

Related

• A remark on compact Kähler manifolds with nef anticanonical bundles and its applications
• Manifolds with nef anticanonical bundle
• On compact Kähler manifolds with pseudo-effective tangent bundle
• Locally Constant Fibrations and Positivity of Curvature
• On compact Kähler manifold with strongly pseudo-effective tangent bundle