10 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…

Many Fano 3-fold codimension 2 weighted complete intersections are birational to special Fano 3-fold hypersurfaces. The birational-model conjecture. A statement analogous to the pa…

A quasismooth member is a quasismooth Fano 3-fold weighted hypersurface belonging to one of the 95 known families of Fano 3-fold weighted hypersurfaces. The uniqueness conjecture.…

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…

Let $X$ be the weighted hypersurface constructed in the source, and let $G$ be the specified cyclic subgroup acting freely in codimension one on $X$, of order $m$. Since $X$ is Cal…

Let $a,b,c$ be positive pairwise coprime integers, let $\mathbb P(a,b,c)$ be the corresponding weighted projective plane, and let $\pi\colon X(a,b,c)\to\mathbb P(a,b,c)$ be the blo…

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…