Upper Bounds on the Turán Density of Hypergraphs Associated with the Projective Plane over a Finite Field

Let $\PG(2,q)$ denote the projective plane over the finite field $\mathbb{F}_q$ where $q\geq2$ is a prime power. For a positive integer $t$, let $B_{t}[\PG(2,q)]$ denote the $t$-page book obtained from $t-$many copies of the $(q+1)-$graph $\PG(2,q)$, sharing a common edge. Employing the $\mathsf{L}^