# Canonical bundle formula and degenerating families of volume forms

@article{Kim2019CanonicalBF, title={Canonical bundle formula and degenerating families of volume forms}, author={Dano Kim}, journal={arXiv: Algebraic Geometry}, year={2019} }

For a degenerating family of projective manifolds, it is of fundamental interest to study the asymptotic behavior of integrals near singular fibers. In our main results, we determine the volume asymptotics (equivalently the asymptotics of $L^2$ metrics) in all base dimensions, which generalizes numerous previous results in base dimension 1. In the case of log Calabi-Yau fibrations, we establish a metric version of the canonical bundle formula (due to Kawamata and others): the $L^2$ metric…

## 3 Citations

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We extend the study of jumping numbers of multiplier ideals due to Ein– Lazarsfeld–Smith–Varolin from the algebraic case to the case of general plurisubharmonic functions. While many properties…

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