Gupta's three-set polynomial Sylvester–Gallai conjecture

Let $R$, $B$, and $G$ be finite disjoint sets of irreducible homogeneous polynomials in $\mathbb{C}[x_1,\ldots,x_n]$ of degree at most $r$. Assume that for every pair $Q_1,Q_2$ from distinct sets, there is a polynomial $Q_3$ in the remaining set such that whenever $Q_1$ and $Q_2$ vanish, $Q_3$ also vanishes; the polynomials are pairwise linearly independent as noted in the source.

Gupta's three-set polynomial Sylvester–Gallai conjecture. There is a function $\lambda(r)$ such that

$$\operatorname{trdeg}_{\mathbb{C}}(R\cup B\cup G)\leq\lambda(r).$$

For $r=1$ this is the Edelstein–Kelly theorem. The source says the conjecture was open for degrees greater than one and proves the quadratic case, again with the stronger conclusion that the linear span has bounded dimension.