Singular Nakano positivity of direct image sheaves of adjoint bundles

2024/07/16 by Takahiro Inayama, Inayama, Takahiro, Shin‐ichi Matsumura +3
Mathematics · Medicine · #32L20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracerebral and Subarachnoid Hemorrhage Research #Primary 32U05 #Secondary 32A70

paper · pdf · doi:10.48550/arxiv.2407.11412

openalex publication_date 2024/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider a proper Kähler fibration f \colon X → Y and a singular Hermitian line bundle (L, h) on X with semi-positive curvature. We prove that the direct image sheaf f_*(O_X(K_X/Y+L) ⊗ I(h)), equipped with the Narasimhan-Simha metric, is singular Nakano semi-positive in the sense that the ∂-equation can be solved with optimal L²-estimate. Our proof does not rely on the theory of Griffiths positivity for the direct image sheaf.

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