Notes on rational chain connectedness
arXiv:2602.19415
The paper extends the Hacon–McKernan rational chain connectedness theorem to complex analytic spaces and shows that fibers of resolutions of complex analytic klt singularities are rationally chain connected, using the minimal model program instead of extension theorems.
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.
22 pages, v2: I have added Lemma 4.6 and corrected the proof of Lemma 5.2, v3: major revisions following the referee's report, v4: I have corrected Lemma 4.2