Generalized K\"ahler-Ricci flow and the classification of nondegenerate generalized K\"ahler surfaces

TL;DR

This paper investigates the generalized K"ahler-Ricci flow on complex surfaces with nondegenerate Poisson structures, establishing long-term existence and convergence to weak hyperK"ahler structures, advancing understanding of geometric flows in complex geometry.

Contribution

It proves long-time existence and convergence of the generalized K"ahler-Ricci flow on nondegenerate generalized K"ahler surfaces, linking it to hyperK"ahler geometry.

Findings

Flow exists for all time on these surfaces

Flow converges to a weak hyperK"ahler structure

Provides classification results for such surfaces

Abstract

We study the generalized K\"ahler-Ricci flow on complex surfaces with nondegenerate Poisson structure, proving long time existence and convergence of the flow to a weak hyperK\"ahler structure.