39 problems

Let $P(a_1,\dots,a_N\mid k_1,\dots,k_m)$ be a nonsingular complete intersection in weighted projective space. Let $t^p(x^*)$ be the mirror maps defined from the genus-zero virtual…

Let $G$ be a crystallographic complex reflection group, meaning a subgroup of $\operatorname{AGL}_n(\mathbb C)$ generated by reflections that fix a hyperplane pointwise and have co…

Let $\mathbb{P}^{\mathbf{w}}$ be the weighted projective space with weights $\mathbf{w}=(w_0,\ldots,w_n)$, and let $I(t)$ be the formal $I$-function defined by … Let the associated…

Let $M={\mathbb C}P^2(N_1,N_2,N_3)$ be a four-dimensional weighted projective space with isolated singularities, equipped with a Kähler metric. The weights are $N_1,N_2,N_3$. Spect…

Explicit invariant formula. The orbifold three-point invariant is

Let $\Phi$ be a family of primitive Fano complete intersections in a weighted projective space, and let $F\in\Phi$ be a general member. Condition (C) conjecture. The variety $F$ sa…

Let an infinite series of anticanonically embedded quasi smooth Fano hypersurfaces in weighted projective 4-spaces be given. The series in the known classification have the form ……

Let $WSP(1,\ldots,1|m)$ denote the weighted superprojective space with $m$ bosonic weights equal to $1$ and fermionic weight $m$. The super Calabi–Yau conjecture. For $m>2$,…

Let $C$ be a non-degenerate integral curve in the weighted projective space $\mathbf{P}(1,1,m,n)$, where $m$ and $n$ are positive integers. Write $n\bmod m$ for the remainder on di…

Let $\operatorname{WPRM}_d(w)$ denote the weighted projective Reed–Muller code of weighted degree $d$ over $\mathbb{F}_q$, where $w=(w_0,\dots,w_m)$ is the weight vector, and let…

Let $S$ be a quasi-smooth, well-formed del Pezzo hypersurface of degree $d$ in the weighted projective space … where $S$ is defined over an algebraically closed field $\Bbbk$ of ch…

Let $W$ be a smooth weighted variety in $\mathbb{WP}^n_{\mathbf{q}}(k)$ with weights $\mathbf{q}=(q_0,\ldots,q_n)$, let $q=\operatorname{lcm}(q_0,\ldots,q_n)$, and let $A$ be an am…

Let $e_q(d;2,3,5)$ be the maximum number of zeros on $\mathbb{P}(2,3,5)(\mathbb{F}_q)$ of a weighted-homogeneous polynomial of weighted degree $d$. Maximum-zero conjecture for weig…

Let $w=(w_0,w_1,ots,w_m)\in\mathbb{N}_{\geq 1}^{m+1}$, let $\mathbb{P}(w)$ be the weighted projective space over $\mathbb{F}_q$, and let $e_q(d;w_0,w_1,\dots,w_m)$ denote the maxim…

Let $X$ be an $n$-dimensional $\delta 835\dcb$-Gorenstein toric variety of rank $r$ and Gorenstein index $k\ge 2$. Let $Q^\circ$ be the polar weight matrix defined in the source, a…

Weighted-projective-space characterization conjecture. If, for every such $\ell$, $g$, and $f$,

d'Horace conjecture. The méthode d'Horace, or a simple modification of it, applies in weighted projective space.

Let $q$ be a prime power, let $a_0,ots,a_n$ be positive weights, and let $e_q(d;a_0,a_1,ots,a_n)$ be the maximum number of ${\mathbb F}_q$-rational points on a hypersurface of weig…

For each integer $n\geq 2$, let $m'_n$ and $E_n$ be the explicitly defined integers associated with the weighted hypersurface construction. Two integers are relatively prime if the…

Let $(X,B)$ be a projective log canonical pair of dimension $n$, where $B$ is a nonzero reduced divisor and $K_X+B$ is ample. The volume of $K_X+B$ is the top self-intersection num…

For each integer $n\geq2$, let $V/G$ be the quotient of the hypersurface constructed in the paper by the cyclic group action described there; it is a klt Calabi–Yau variety of dime…

The examples under consideration are klt Calabi–Yau varieties obtained as quotients of quasismooth Calabi–Yau hypersurfaces in weighted projective spaces by finite groups, and thei…

Let $\Gamma$ be a crystallographic $r$-group, let $T$ be its subgroup of translations, and set $A=\mathbb{C}^n/T$. Then $\mathbb{C}^n/\Gamma=A/K$, where $K$ is the induced finite l…

Let $\Lambda_W$ be the suitable lattice associated to a finite irreducible Weyl group $W$, and let $E$ be an elliptic curve. The quotient is $\Lambda_W\otimes E/W$. Characteristic-…

Minimal-volume conjecture. For every integer $n\geq 2$, $X_n$ has the minimum volume among all klt projective $n$-folds with ample canonical class.