MathOverflow

I encounter the following problem in my research. It seems that we can bound a positive $(m,m)$ form by the wedge product of a factor from the base manifold with a $(m-1,m-1)$ form when $m$ is larger than the dimension of fiber.
Let $(X, \omega_X)$ and $(Y,\omega_Y)$ be compact Kaehler manifolds and $f: X\to Y$ be a surjective holomorphic map between $X$ and $Y$....

In the Atiyah problem on configurations of points, one defines smooth complex-valued functions $D(\mathbf{x}_1, \ldots, \mathbf{x}_n)$ on the configuration space of $n$ distinct points in $\mathbb{R}^3$ (more precisely, $\mathbf{x}_i \in \mathbb{R}^...

Let $m$ and $n$ be positive integers, and let $m<n$. Let $A$ be an $m \times n$ real matrix. TheMoore--Penrose inverse $A^+$ of $A$ is a unique $n \times m$ matrix satisfyingthe following four equations:\begin{align}\label{eq:mp}AA^{+}A=A, \quad...

I have asked the same question here in math stack-exchange but have not received any answer. So I would like to ask the same here.Given a homomorphism $\phi:\mathbb{Z}_n \to \operatorname{Aut}(\mathbb{Z}_m)$, one can construct the semi-direct product...