IGA: Legendre Transforms Convex Functions and Plurisubharmonic Metrics
Channel: UMD Mathematics
Date: 03/11/2021

Rémi Reboulet (Grenoble)
Abstract:
We begin by explaining the correspondence between convex functions on integral polytopes and plurisubharmonic (i.e. "generalized convex") metrics on polarized toric varieties. Under this correspondence, geodesics in the space of toric psh metrics are transformed into affine segments of convex functions. We then show how this result can be extended to more general geodesics of plurisubharmonic metrics in the non-toric case, using a construction of Witt Nyström. If time permits, we will also look into some non-Archimedean aspects of this generalized result, applied to geodesic rays.