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

TL;DR

This paper extends the canonical bundle formula to complex analytic fibrations with irrational coefficients and non-compact bases, and explores boundedness of complements in this context.

Contribution

It introduces a generalized canonical bundle formula for complex analytic fibrations with irrational coefficients over non-compact bases.

Findings

Established the generalized canonical bundle formula in the complex analytic setting.

Demonstrated compatibility of discriminant and moduli b-divisors with restriction to open subsets.

Discussed boundedness of complements in the 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.