Special representatives of complexified K\"ahler classes

Abstract

Motivated by constructions appearing in mirror symmetry, we study special representatives of complexified K\"ahler classes, which extend the notions of constant scalar curvature and extremal representatives for usual K\"ahler classes. In particular, we provide a moment map interpretation, discuss a possible correspondence with compactified Landau-Ginzburg models, and prove existence results for such special complexified K\"ahler forms and their large volume limits in certain toric cases.