Rational chain connectedness in the complex analytic setting
Osamu Fujino
Journal of Singularities
volume 29 (2026), 234-253
Received: 5 March 2026. In revised form: 15 July 2026
Abstract:
We extend Hacon-McKernan'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.
2020 Mathematical Subject Classification:
Primary 14E30; Secondary 14J17, 32S05
Key words and phrases:
complex analytic spaces, rational chain connectedness, rational connectedness, kawamata log terminal singularities, minimal model program
Author(s) information:
Osamu Fujino
Department of
Mathematics
Graduate School of Science
Kyoto University
Kyoto 606-8502, Japan
email: fujino@math.kyoto-u.ac.jp