Dissertation Defense: Convergence of measures on non-Archimedean hybrid spaces

Abstract: We study the convergence of certain classes of complex geometric measures to certain non-Archimedean measures. This convergence takes place on the non-Archimedean hybrid space introduced by Boucksom and Jonsson. Given a family X of complex analytic spaces parametrized by the punctured unit complex disk, the hybrid space associated to this family is a partial compactification of this family obtained by filling in the puncture with the Berkovich analytification of X. Furthermore, if each of the complex analytic spaces in the family carry a natural measure, we can think of these measures as being supported on the hybrid space, then their weak limit is a measure supported on the Berkovich space.

First, we study the convergence of volume forms on a degenerating holomorphic family of log Calabi–Yau varieties, extending a result of Boucksom and Jonsson. Secondly, we prove a folklore conjecture that the Bergman measures along a holomorphic family of curves parametrized by the punctured unit disk weakly converge to the Zhang measure on the associated Berkovich space.

Hybrid Defense:
271 Weiser Hall
https://umich.zoom.us/j/93673413700?pwd=clQ0eVBFZDI4eXBXTVBtOHFPbTNmdz09
Meeting ID: 936 7341 3700
Passcode: thesis