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Recently Antonio Alarcón proved that in the case of the unit ball $B\subset\mathbb{C}^n$ for $n\geq 2$ every smooth closed complex submanifold of dimension $q\leq n$, $V\subset\mathbb{C}^n$ defines a ...

Let $X$ be a complex compact manifold of complex dimension $n$. Let $K_X$ denote its canonical class. Is it true that the cohomology group $$H^n(X,K_X)$$ is one dimensional? Remark. If $X$ is Kähler ...

hallo, my problem is the following: i have a finite sequence of holomorphic $k-$forms $\alpha_{k}$, each defined on open subsets $U_{k} \subset M$, where $M$ is a complex $n$-dimensional manifold, ...