Moraga–Yeong algebraic hyperbolicity conjecture

Let $X$ be a smooth projective variety of dimension $n\geq 2$, let $K_X$ be its canonical line bundle, and let $L$ be an ample line bundle on $X$. Moraga–Yeong's conjecture. The complete linear system

$$|K_X+(3n+1)L|$$

is algebraically hyperbolic, meaning that a very general member is algebraically hyperbolic. The conjecture concerns the converse direction to the relationship between Kobayashi and algebraic hyperbolicity and remains open in general.