7 problems

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…

Let $q=t^2$ with $t$ a prime power, and let $X\subset\mathbb{P}^3$ be the hermitian surface … For a form $f$ of degree $h\leq t$, write $Z(f)$ for its zero locus and…

Conjecture on the fourth and fifth weight. The quantities $s_4(t)$ and $s_5(t)$ should give, respectively, the fourth and the fifth weight of the code.

Cossidente–Siciliano's conjecture. Every special set of $\mathsf{H}(3,q^2)$ is classical, meaning equivalent under the collineation group of $\mathsf{H}(3,q^2)$ to $\mathcal{V}$.

Class-number conjecture. If

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

Let $q$ be a prime power, let $\mathcal U$ be the non-degenerate Hermitian surface in $\operatorname{PG}(3,q^2)$, and let a complete cap be a Hermitian cap maximal with respect to…