3 problems

Class-number conjecture. If

Let $q$ be a prime power, let $F\in\mathbb{F}_{q^2}[x_0,x_1,x_2,x_3]$ be homogeneous of degree $d$, and let $V_2\subset\mathbb{P}^3$ be a non-degenerate Hermitian surface defined o…

Edel–Landjev–Xiang conjecture. For each $i$, there exist linear homogeneous polynomials $H_1,\ldots,H_d$ such that the hyperplanes $V(H_1),\ldots,V(H_d)$ contain a common line and