5 problems

Let $(X^n,\omega)$ be a compact Hermitian manifold and let $\alpha$ be a closed real $(1,1)$-form whose Bott–Chern class $[\alpha]$ is nef. A class is big if it contains a current…

Shenfeld–van Handel's conjecture. One has

Let $X$ be a compact Kähler manifold, let $\Omega$ be a Lorentzian class of dimension $d$ on $X$, and let $\alpha,\beta$ be big nef classes on $\Omega$. Define…

Let $(X^n,\omega)$ be a compact Hermitian manifold and let $\alpha$ be a closed real $(1,1)$-form whose Bott–Chern class $[\alpha]$ is nef. For a smooth real-valued function $u$, w…

Let $M$ be a hyperkähler manifold, and let $\eta$ be a rational nef class on $M$. A nef class is semiample if it is associated with a holomorphic map from $M$ to a complex manifold…