8 problems

Yau's conjecture. These conditions are sufficient for the existence of solutions of the Hull–Strominger system in the case of threefolds.

Let $X$ be a compact Calabi–Yau threefold with holomorphic volume form $\Omega$, and let $\mathfrak{b}_0$ be a balanced class on $X$. Let $V$ be a holomorphic vector bundle over…

Yau's conjecture. There is a solution of the full Hull–Strominger system on $X$.

Kähler-potential conjecture. The function $K$ defines the Kähler potential for a Kähler metric on this moduli space.

Let $(X,P)$ be a Calabi–Yau threefold with bundle $P$ admitting a solution of the Hull–Strominger system. Let $\dot{\mathfrak{a}}\in H^{1,1}_A(X)$ and…

Let $D$ be the domain of the potential function $F:D\to\mathbb{R}$ associated with the period map for the stated ansatz, where $F$ is strictly convex and satisfies…

Yau's conjecture. The triple $(X,\Omega,P)$ admits a solution of the Hull–Strominger system.

Let $V$ be the conserved vector … which parameterizes the conformally balanced cohomology class for the generalized Calabi–Gray ansatz. A solution of the Hull–Strominger system is…