7 problems

Polarized semiclassical Yau–Tian–Donaldson conjecture. The following are equivalent:

Semiclassical Yau–Tian–Donaldson conjecture. The triple $(X,\sigma,\alpha)$ is Poisson K-polystable if and only if there exists $\epsilon>0$ such that, for every…

Generalized Kähler–Ricci-flow convergence conjecture. The generalized Kähler–Ricci flow preserves the generalized Kähler class, exists for all time, and converges to the unique gen…

Generalized Kähler Calabi–Yau conjecture. There exists a unique generalized Calabi–Yau geometry $(g_{CY},b_{CY},I,J_{CY})\in[(g,b,I,J)]$, and furthermore $(g_{CY},I)$ and…

Suppose $(g, I, J)$ is a symplectic type generalized Kähler structure on a Fano manifold $(M, J)$, with $F \in 2\pi c_1(M, J)$. Let $(g_t,I_t,J)$ be the solution of the normalized…

Let $(M^{4n}, g, I, J)$ be a nondegenerate generalized Kähler manifold, and consider its $\Omega$-Hamiltonian deformation class. Generalized Kähler Calabi–Yau conjecture. There exi…

Let $(M^{2n},g,J_\pm)$ be a generalized Kähler structure satisfying $[J_+,J_-]=0$. Let $\mathcal H$ be the space of formally generalized Kähler classes, and let $P$ be the associat…