Higher-dimensional doubly ruled incidence conjecture for algebraic curves

Let $\Gamma$ be a set of $L$ irreducible algebraic curves in $\mathbb{C}^n$, each of degree at most $d$, and let $P_2(\Gamma)$ denote the set of points incident to at least two curves of $\Gamma$. Higher-dimensional doubly ruled incidence conjecture for algebraic curves. Either

$$|P_2(\Gamma)|\leq C(d,n)L^{\frac{n}{n-1}},$$

or there exist an integer $m$ with $2\leq m\leq n-1$ and an irreducible affine variety $Z$ of dimension $m$ which is generically doubly ruled by algebraic curves of degree at most $d$ and contains at least $L^{\frac{m-1}{n-1}}$ curves of $\Gamma$. This is the curve analogue of the line conjecture and extends the proposed higher-dimensional incidence alternative beyond straight lines; the source presents it as a conjectural generalization, with no resolution supplied.