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Classification of Smooth Minimal Kähler Fourfolds Without Effective Divisors and Surfaces
Abstract
We prove the following two statements: (1) If X is a compact Kähler fourfold with pseudo-effective canonical bundle and no subvarieties of codimension one or two, then KX is a torsion line bundle; (2) If X is a compact Kähler fourfold with no subvarieties of codimension one or two, then X is not uniruled. Using the Beauville-Bogomolov decomposition and a characterization of Uniruled manifolds by Wenhao Ou, we get that if X is a compact Kähler fourfold with no subvarieties of codimension one or two, then either X is a torus or an irreducible holomorphic symplectic manifold.
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BibTeX
@misc{vikash2026classification,
title = {{Classification of Smooth Minimal Kähler Fourfolds Without Effective Divisors and Surfaces}},
author = {Pisya Vikash},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.04536},
eprint = {2607.04536},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.04536},
}
RIS
TY - UNPB
TI - Classification of Smooth Minimal Kähler Fourfolds Without Effective Divisors and Surfaces
AU - Pisya Vikash
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2607.04536
UR - https://arxiv.org/abs/2607.04536
AB - We prove the following two statements: (1) If X is a compact Kähler fourfold with pseudo-effective canonical bundle and no subvarieties of codimension one or two, then K_X is a torsion line bundle; (2) If X is a compact Kähler fourfold with no subvarieties of codimension one or two, then X is not uniruled. Using the Beauville-Bogomolov decomposition and a characterization of Uniruled manifolds by Wenhao Ou, we get that if X is a compact Kähler fourfold with no subvarieties of codimension one or two, then either X is a torus or an irreducible holomorphic symplectic manifold.
ER -