6 problems

A polarized Calabi–Yau manifold is a pair $(X,\omega)$ consisting of a compact algebraic manifold $X$ with zero first Chern class and a Kähler form $\omega\in H^2(X,\mathbb Z)$. Le…

A special Kähler manifold is a Kähler manifold equipped with the additional differential-geometric structure arising as the base of an algebraically completely integrable Hamiltoni…

Let the moduli space of a Calabi–Yau threefold be equipped with its Weil–Petersson geometry, and consider its geodesics. Stability conjecture. All Weil–Petersson geodesics on the m…

Let $d$ denote the dimension parameter in the collapsing hyperkähler construction, and suppose the associated singular special Kähler metric arises under the uniform energy bound c…

Let $frak b=(\beta_1,dots,\beta_k)$ be a tuple as in Definition ref{defn:moduli}, and let $gamma>1$ be an integer. Assume that the numerical condition eqref{EqNecessCondMixedSing}…

Canonical Hamiltonian conjecture. The canonical choice of Hamiltonian yields the Ferrara–Sabharwal metric, up to a factor.