The nondegenerate generalized Kähler Calabi–Yau problem

Abstract We formulate a Calabi–Yau-type conjecture in generalized Kähler geometry, focusing on the case of nondegenerate Poisson structure. After defining natural Hamiltonian deformation spaces for structures generalizing notion class, we unique solvability Gualtieri’s Calabi–Yau equation within this class. establish uniqueness, and moreover show that all such solutions are actually hyper-Kähler metrics. furthermore GIT framework problem, interpreting as zeroes moment map associated to action finding Kempf–Ness functional. Lastly indicate naturality Kähler–Ricci flow setting, showing it evolves given functional is monotone, so only possible fixed points On background, global existence weak convergence flow.