17 problems

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 $S$ 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 $w=(w_0,w_1,ots,w_m)\in\mathbb{N}_{\geq 1}^{m+1}$, 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 $P(a_1,\dots,a_N\mid k_1,\dots,k_m)$ be a nonsingular complete intersection in weighted projective space. Let $t^p(x^*)$ be the mirror maps defined from the genus-zero virtual…

Let $X$ 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 $f$,

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…

Let $\Gamma$ and $\Gamma_1$ be commensurable complex crystallographic groups acting on $\mathbb{C}^n$, with equal linear parts $\mathrm{d}\Gamma_1=\mathrm{d}\Gamma$. Assume that…

Let $d,e\geq 2$ be relatively prime integers and let $r,s\geq 2$. Let $\mathbb{P}(\underbrace{d,\ldots,d}_{r},\underbrace{e,\ldots,e}_{s})$ denote the weighted projective space wit…

Let $\mathbb{P}(a_0,a_1,\ldots,a_m)$ be a weighted projective space over $\mathbb{F}_q$, let $e_q(d;1,a_1,a_2,\ldots,a_m)$ be the minimum number of $\mathbb{F}_q$-rational zeros of…

Let a weighted projective space be a projective toric variety, and call it defective when its dual variety is not a hypersurface. A cone over a weighted projective space is a weigh…

Let the GHV model be associated with a smooth hypersurface satisfying the assumptions of theorem, and let $n$, $d$, and $w$ be the parameters appearing there, with $n+d-w>0$. A com…

Let $N_\delta(d,m;y)$ be the polynomial from the weighted-projective refined node polynomial conjecture, let $\widetilde N^{(\Sigma_m,dH),\delta}(y)$ be the refined invariant on th…