Bogomolov Decomposition and Compact K{ä}hler Manifolds of Algebraic Dimension Zero

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1. Verfasser: Campana, Frederic Bruno
Format: Preprint
Veröffentlicht: 2026
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author Campana, Frederic Bruno
author_facet Campana, Frederic Bruno
contents We prove conditionally that compact K\''ahler manifolds of algebraic dimension zero are (essentially) isogeneous to products of Kummer and `simple' ones, the latter being conjecturally bimeromorphically symplectic. `Simple' means: its general point is not contained in a nontrivial subvariety. We also prove that four-dimensional `strictly simple' manifolds are either étale quotients of tori or holomorphically symplectic. `Strictly simple' means: its only subvarieties are points and itself.
format Preprint
id arxiv_https___arxiv_org_abs_2605_19713
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Bogomolov Decomposition and Compact K{ä}hler Manifolds of Algebraic Dimension Zero
Campana, Frederic Bruno
Algebraic Geometry
We prove conditionally that compact K\''ahler manifolds of algebraic dimension zero are (essentially) isogeneous to products of Kummer and `simple' ones, the latter being conjecturally bimeromorphically symplectic. `Simple' means: its general point is not contained in a nontrivial subvariety. We also prove that four-dimensional `strictly simple' manifolds are either étale quotients of tori or holomorphically symplectic. `Strictly simple' means: its only subvarieties are points and itself.
title Bogomolov Decomposition and Compact K{ä}hler Manifolds of Algebraic Dimension Zero
topic Algebraic Geometry
url https://arxiv.org/abs/2605.19713