Fundamental groups of compact Kähler manifolds with semi-positive holomorphic sectional curvature
Year: 2026
Type: article
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 $\phi \colon X \to Y$ 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 ) $\pi _{1}(X)$ pi 1 left parenthesis upper X right parenthesis , with a focus on varieties of special type.
Source: Forum of Mathematics Sigma
Author: Shin-ichi Matsumura
Institution: Tohoku University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,650
OpenAlex ID: W4407123465