5 problems

Ample-normal-bundle conjecture. The algebraic dimension of $X$ should be at least one greater than the dimension of any positive-dimensional compact submanifold with ample normal b…

Isotriviality conjecture for simple fibres. If $X_y$ is simple and $a(Y)=0$, then

Let $X$ be a compact hyperkähler manifold of dimension $2n$, and let $a(X)$ denote its algebraic dimension. Algebraic-dimension values conjecture. Then … The source reports that th…

Let $X$ be a non-projective compact hyperkähler manifold and let $L$ be a non-trivial nef line bundle. Let $a(X)$ be the transcendence degree of the field of meromorphic functions…

Algebraic-dimension conjecture. One has