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Let $M$ be a compact complex surface, i.e., a complex manifold with complex dimension two. Also, let us denote its Kähler metric by $g$ and its Kähler form by $K$. Let us denote the Kähler class by $[...

Let $X$ be a strict compact Calabi-Yau manifold of dimension $n$. By this, I mean that $X$ is a simply connected projective manifold whose holomorphic forms are generated by a nowhere zero top degree ...

By a threefold, I mean a compact complex manifold of dimension three. For a simply-connected threefold with trivial canonical class, its Betti numbers satisfy: $$b_2 \ge 0, b_3 \ge 2.$$ I am wondering ...