Classification of Generalized Kahler-Ricci Solitons on Complex Surfaces

Using toric geometry we give an explicit construction of the compact steady solitons for pluriclosed flow first constructed in by the first author in 2019. This construction also reveals that these solitons are generalized Kahler in two distinct ways, with vanishing and nonvanishing Poisson structure. This gives the first examples of generalized Kahler structures with nonvanishing Poisson structure on nonstandard Hopf surfaces, completing the existence question for such structures. Moreover, this gives a complete answer to the existence question for generalized Kahler-Ricci solitons on compact complex surfaces. In the setting of generalized Kahler geometry with vanishing Poisson structure, we show that these solitons are unique. We show that these solitons are global attractors for the generalized Kahler-Ricci flow among metrics with maximal symmetry. (c) 2020 Wiley Periodicals LLC