Albanese morphism of log smooth klt compact K\"ahler manifold with nef log anticanonical divisor

Xiaojun Wu

Albanese morphism of log smooth klt compact K\"ahler manifold with nef log anticanonical divisor

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arxiv 2301.05194 v1 pith:2PKVFWXI submitted 2023-01-12 math.CV math.AG

Xiaojun Wu This is my paper · ORCID

classification math.CVmath.AG

keywords betaahleralbanesecompactdivisormanifoldanalyticanticanonical

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abstract

Let $(X, \omega)$ be an n-dimensional compact K\"ahler manifold. Let $D=\sum (1-\beta_j) Y_j=\sum (1-\beta_j) [s_j=0]$ a divisor with simple normal crossings with $\beta_j \in ]0,1[$ such that $-(K_X+D)$ is nef. We show that its Albanese map is submersion outside an analytic set of codimension larger than two with connected fibres.

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Compact K\"ahler manifolds with nef anti-canonical bundle
math.AG 2025-06 conditional novelty 7.0 of 10

Every compact Kähler manifold with nef anti-canonical bundle admits a locally trivial fibration over a Calabi-Yau manifold with rationally connected fibers.

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