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arXiv · 2605.19713

Bogomolov decomposition and compact K{\"a}hler manifolds of algebraic dimension zero

Frederic Bruno Campana
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Abstract

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 \'etale quotients of tori or holomorphically symplectic. `Strictly simple' means: its only subvarieties are points and itself.

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Frederic Bruno Campana. 2026-05-19. Bogomolov decomposition and compact K{\"a}hler manifolds of algebraic dimension zero. https://arxiv.org/abs/2605.19713

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