Mattias Jonsson: Base loci of linear series and non-Archimedean Monge–Ampère equations

Abstract: Yau proved that every Calabi–Yau manifold admits a Ricci flat metric. He did this by solving a complex Monge–Ampère equation. Recently, Yang Li proved that the regularity of a solution to an analogous non-Archimedean Monge–Ampère equation has implications for the SYZ conjecture in mirror symmetry. I will provide both positive and negative evidence for such a regularity. The negative evidence is based in part on a construction by Lesieutre of an effective divisor with Zariski dense diminished base locus.