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arXiv · 2607.04536

Classification of Smooth Minimal K\"ahler Fourfolds Without Effective Divisors and Surfaces

Pisya Vikash
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Abstract

We prove that if \(X\) is a compact K\"ahler fourfold with pseudo--effective canonical bundle and no subvarieties of codimension one or two, then \(K_X\) is a torsion line bundle. By the Beauville--Bogomolov decomposition theorem, it follows that \(X\) is either a quotient of a complex torus or an irreducible holomorphic symplectic manifold.

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Pisya Vikash. 2026-07-05. Classification of Smooth Minimal K\"ahler Fourfolds Without Effective Divisors and Surfaces. https://arxiv.org/abs/2607.04536

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