Radical Sylvester–Gallai conjecture

Let $\rK$ be the base field. For $d\in\N$, an $\rsg{d}$ configuration is a configuration $\cF$ of polynomials as defined in the cited formulation of Gupta's conjecture; its transcendence degree is taken over $\rK$. Radical Sylvester–Gallai conjecture. There is a function

$$\lambda: \N \to \N$$

such that the transcendence degree of any $\rsg{d}$ configuration $\cF$ is at most $\lambda(d)$. This is the first non-linear analogue of the linear Sylvester–Gallai problem and is intended to give bounded algebraic complexity to radical Sylvester–Gallai configurations; the source refers to external works for the precise definition, and its status is not resolved here.