3 problems

Let $X$ be a compact complex manifold of dimension $3$ with holomorphic volume form $\Omega$. Let $\omega$ be a Hermitian metric satisfying … and denote its balanced class by…

Let $(X,\Omega)$ be a compact Calabi-Yau threefold endowed with a balanced class $\tau$. Let $\mathcal{E}$ be a holomorphic vector bundle over $X$ satisfying $c_1(\mathcal{E})=0$ a…

Let $X$ be a homologically balanced Calabi--Yau threefold, let $V$ be a stable holomorphic vector bundle over $X$, and write $c_2(V)$ and $c_2(X)$ for their second Chern classes. Y…