• Corpus ID: 204576113

Canonical bundle formula and degenerating families of volume forms

  title={Canonical bundle formula and degenerating families of volume forms},
  author={Dano Kim},
  journal={arXiv: Algebraic Geometry},
  • Dano Kim
  • Published 15 October 2019
  • Mathematics
  • arXiv: Algebraic Geometry
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… 

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