10 problems

Green–Griffiths conjecture. Every entire curve $f\colon\mathbb C\to X$ in a projective manifold $X$ of general type is algebraically degenerate.

Brück's conjecture. If

Let $f:\mathbb{C}\to\mathbb{P}^n(\mathbb{C})$ be an algebraically nondegenerate holomorphic curve, and let the hypersurfaces be in general position. Shiffman's conjecture. The tota…

Let $f:8?\mathbb{C}\to\mathbb{P}^n(\mathbb{C})$ be a holomorphic curve whose image spans a linear subspace of codimension $s$, and let $H_j$, $j=0,\ldots,q$, be hyperplanes as in C…

Wronskian generalization conjecture. In general, the Wronskian $W(f)$ should be replaced by a generalization of it, still of Wronskian type; if so, the expected truncation level is

Green's conjecture. If $f$ omits $D$, then $f(\mathbf{C})$ is algebraically degenerate; equivalently, the conclusion of Green's theorem for finite-order holomorphic curves should h…

Zhang et al.'s conjecture. If $f$ and $\Delta^n f$ share $0$ CM, then $f$ has the form

Liu–Laine's conjecture. If $f$ and $\Delta_c^n f$ share $a\in\mathbb{C}\backslash\{0\}$ CM, then

Let $X=\mathbb{P}^n$ and let $f:\mathbb{C}\rightarrow\mathbb{P}^n$ be an entire holomorphic curve whose image is not contained in any hyperplane. Let $T_f(r)$ be the characteristic…

Orbifold Cartan conjecture. If