EVENT DETAILS AND ABSTRACT

Title: Degenerations of Calabi-Yau manifolds and non-Archimedean geometry
Speaker: Sébastien Boucksom
Speaker Info: Université Pierre et Marie Curie
Brief Description:
Special Note:
Abstract:

I will present joint work in progress with Mattias Jonsson. Kontsevich and Soibelman have given a conjectural description of the Gromov-Hausdorff limit of a maximally degenerate family of polarized Calabi-Yau manifolds in terms of the Berkovich space attached to the degeneration. Motivated by this, Mustata, Nicaise and Xu recently studied the essential skeleton of this Berkovich space, which is a natural realization of the dual complex of a minimal model of the degeneration. We show that the volume form induced by a holomorphic form of top degree on a fiber converges, in some appropriate sense, to an explicit Lebesgue type measure on the essential skeleton.