Peer-reviewedCC BY 4.0Forum of Mathematics, Sigma
Fundamental groups of compact Kähler manifolds with semi-positive holomorphic sectional curvature
- 1Graduate School of Science, Tohoku University
Abstract
In this paper, we prove that a compact Kähler manifold X with semi-positive holomorphic sectional curvature admits a locally trivial fibration ϕ : X → Y ϕ : X → Y phi colon upper X right arrow upper Y , where the fiber F is a rationally connected projective manifold and the base Y is a finite étale quotient of a (compact complex) torus. This result extends the structure theorem, previously established for projective manifolds, to compact Kähler manifolds. A key part of the proof involves analyzing the foliation generated by truly flat tangent vectors and showing the abelianness of the topological fundamental group π 1 ( X ) π 1(X) pi 1 left parenthesis upper X right parenthesis , with a focus on varieties of special type.
Related
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BibTeX
@article{matsumura2026fundamental,
title = {{Fundamental groups of compact Kähler manifolds with semi-positive holomorphic sectional curvature}},
author = {Shin-ichi Matsumura},
journal = {Forum of Mathematics, Sigma},
year = {2026},
month = oct,
doi = {10.1017/fms.2026.10286},
url = {https://www.cambridge.org/core/product/identifier/S2050509426102862/type/journal_article},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Fundamental groups of compact Kähler manifolds with semi-positive holomorphic sectional curvature
AU - Shin-ichi Matsumura
PY - 2026
DA - 2026/10/14
JO - Forum of Mathematics, Sigma
DO - 10.1017/fms.2026.10286
UR - https://www.cambridge.org/core/product/identifier/S2050509426102862/type/journal_article
AB - In this paper, we prove that a compact Kähler manifold X with semi-positive holomorphic sectional curvature admits a locally trivial fibration ϕ : X → Y ϕ : X → Y phi colon upper X right arrow upper Y , where the fiber F is a rationally connected projective manifold and the base Y is a finite étale quotient of a (compact complex) torus. This result extends the structure theorem, previously established for projective manifolds, to compact Kähler manifolds. A key part of the proof involves analyzing the foliation generated by truly flat tangent vectors and showing the abelianness of the topological fundamental group π 1 ( X ) π _1(X) pi 1 left parenthesis upper X right parenthesis , with a focus on varieties of special type.
SN - 2050-5094
ER -