Rational chain connectedness in the complex analytic setting

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.

arXiv comment22 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, v5: title changed. Final version accepted for publication in Journal of Singularities