| Résume | For a family of compact complex manifolds, the direct image of the canonical bundle (or Hodge bundle) admits a natural metric. Approaching singular fibers this metric degenerates, and we provide explicit expressions for the dominant terms in the Calabi-Yau case. These are described in terms of topological invariants coming from vanishing cycles or limit Hodge structures. If time permits I will discuss applications to BCOV-torsion which first arose in mirror symmetry. |
