4 problems

Let $Y$ be a compact complex manifold of dimension $n$, let $F$ be a holomorphic line bundle on $Y$, and define … For a smooth closed $(1,1)$-form $\alpha$ in $c_1(F)$, let…

Let $X$ be a compact complex manifold of dimension $n$, and let $H^{1,1}_{BC}(X,\mathbb C)$ denote its complex Bott–Chern $(1,1)$-cohomology. A class is nef if it lies in the nef c…

Let $X$ be a compact complex manifold of complex dimension $n$. Let $\alpha$ be a closed real $(1,1)$-form, and let $X(\alpha,\leq 1)$ be the set where $\alpha$ is nondegenerate an…

Let $X$ be an $n$-dimensional compact complex manifold. For a real $d$-closed $(1,1)$-form $alpha$, let $X(alpha,\leq 1)$ be the set where $alpha$ has at most one negative eigenval…