On generalized canonical bundle formula and boundedness of complements in complex analytic setting

Abstract

We establish the generalized canonical bundle formula for generalized lc-trivial fibrations with irrational coefficients over non-compact bases in the complex analytic setting, and we show that the discriminant b-divisor and moduli b-divisor are compatible with restriction to arbitrary open subsets. We also discuss the boundedness of complements in this setting.

arXiv comment40 pages. This version incorporates the results of arXiv:2606.30983. A detailed proof of Proposition 3.8 has been added. Numerous other revisions to wording and typos have also been made