10 problems

Determine whether, for every countable family of hyperplanes $\{H_j\}_{j\in\mathbb{N}}$ in general position in $\mathbb{P}^m$ and every linearly nondegenerate holomorphic curve…

Irreducibility conjecture. For every $cepsilon>0$, there exists a nonzero negatively twisted invariant logarithmic $2$-jet differential $comega$ in this space with

Let $X$ be a smooth quasi-projective variety. Define the special loci … as follows: $\mathrm{Sp}_{\mathrm{sab}}(X)$ is the Zariski closure of the union of images of non-constant ra…

Griffiths–Lang conjecture. There exists a proper Zariski closed subset $Z_D\subsetneq X$ such that, for all holomorphic curves $\mathbf{x}:\mathbb{C}\to X$ with…

Griffiths' conjecture. (1) For every holomorphic curve $f:\mathbb{C}\to X$ with Zariski-dense image,

Cao and Zheng's tropical Griffiths conjecture. The defect sum satisfies

Vojta's general abc conjecture. (a) If $f:\mathbb C\to X$ is an algebraically nondegenerate analytic map, then

Truncated tropical Cartan conjecture. The displayed truncated second main theorem is proposed as the tropical counterpart of the truncated Cartan second main theorem. The source gi…

Truncated tropical second main theorem conjecture. These truncated inequalities and equality are conjectured to hold as stated. They are tropical analogues of the truncated classic…

Tropical Griffiths-type defect conjecture. One should have