6 problems

Let $X$ be the weighted Fano threefold hypersurface considered in the paper, with numerical parameter $N$, and let $a_{2}$ and $a_{3}$ be the weights defining the weighted projecti…

Let $S=\mathbb{F}_q[x_0,\ldots,x_n]$ be graded by positive weights $w_i$, and let $X=V(F)\subseteq\mathbb{P}(w_0,\ldots,w_n)$ be defined by a nonzero weighted homogeneous polynomia…

Aubry et al.'s point-count conjecture. If $1=w_0\leq w_1\leq w_2\leq\cdots\leq w_n$ and $\operatorname{lcm}(w_1,w_2,\ldots,w_n)\mid d$, then

Let $n\geq2$, let $X$ be the weighted Calabi-Yau hypersurface constructed in the source, and let $G$ be the cyclic subgroup acting freely in codimension one. Let $m=|G|$. Maximal-i…

Fletcher's completeness conjecture. The lists of threefold weighted complete intersections are complete without any degree constraints.

Fletcher's codimension conjecture. There are no canonically embedded threefold complete intersections in WPS of codimension $>5$, and there are no anticanonically embedded…