8 problems

A smooth degeneration of a projective manifold is a smooth proper family whose general fibre is a projective manifold. A compact complex manifold is Moishezon if its algebraic dime…

Let $g:\mathcal X\to\Delta$ be a flat, proper, Moishezon morphism, where $\Delta$ is the unit disc in $\mathbb C$. Assume that $X_0$ has only canonical singularities. A morphism…

Let $g:\mathcal X\to\Delta$ be a flat, proper, Moishezon morphism over the unit disc $Delta a$ in $mathbb C$. Assume that $X0$ has only canonical singularities. A morphism is **fib…

Let $f:\text{?}$ be a family, automatically flat over a smooth curve in this paper, whose fibers all have only canonical singularities. A fiber is Moishezon if it is Moishezon, and…

Let $f\colon X\to\Delta$ be a proper flat morphism over a disk, where $\Delta^*=\Delta\setminus\{0\}$, and write $X_t=f^{-1}(t)$. Assume that $X_t$ is Moishezon for every…

Positive-sheaf characterization conjecture. Moishezon 1-concave manifolds should be characterizable in terms of positive sheaves, analogously to the Grauert–Riemenschneider charact…

Let $\pi:\mathcal{X}\rightarrow Y$ be a holomorphic family of compact complex manifolds over a complex variety $Y$, let $V\subset Y$ be a proper subvariety, and write…

Let $\pi:\mathcal{X}\rightarrow\Delta$ be a holomorphic family of compact complex manifolds of dimension $n$ over an open disk $\Delta\subset\mathbb{C}$, with fibers…