Notes on rational chain connectedness
Algebraic Geometry
2026-03-06 v2
Abstract
We extend Hacon--M\textsuperscript{c}Kernan's rational chain connectedness theorem to the complex analytic setting. As a consequence, we prove that the fibers of any resolution of singularities of complex analytic kawamata log terminal singularities are rationally chain connected. In contrast to the original approach, we avoid the use of extension theorems and instead rely on the minimal model program.
Cite
@article{arxiv.2602.19415,
title = {Notes on rational chain connectedness},
author = {Osamu Fujino},
journal= {arXiv preprint arXiv:2602.19415},
year = {2026}
}
Comments
20 pages, v2: I have added Lemma 4.6 and corrected the proof of Lemma 5.2