11 problems

Let $A=\operatorname{Spec}\bigoplus_{n\geq0}H^0(w\mathbb{P},-nK)$ be the anticanonical affine cone over the weighted projective space $w\mathbb{P}$, and let $\widetilde{A}\to A$ be…

Let $\mathcal{X}$ be a smooth Deligne--Mumford stack with an étale cover $\pi:U\to\mathcal{X}$ by a scheme, and set $Z=U\times_{\mathcal{X}}U$. The correspondence $Z\times_UZ\to Z$…

Let $X$ be a quasiprojective scheme over a field $k$, let $G$ be a finite group acting on $X$, and assume that $\operatorname{char} k$ does not divide $|G|$. Let…

Wang's maximal-Betti-number conjecture. The variety $W^{(n)}$ has the largest sum of Betti numbers among smooth, projective Calabi-Yau $n$-folds. When $n$ is odd, it also has the s…

Let $n$ be a positive integer, and consider projective $n$-dimensional varieties with quotient singularities and trivial canonical class. Write $H$ for the sum of their orbifold Be…

Let $\mathscr{X}$ be a projective symplectic quotient orbifold, and write $H\! H^\bullet(\mathscr{X})$ for its Hochschild cohomology and $H^\bullet_\mathrm{orb}(\mathscr{X})$ for i…

Let $\mathscr{X}$ be a symplectic quotient orbifold and let $\mathscr{A}$ be an appropriate quantization of $\mathscr{X}$. Ginzburg–Kaledin conjecture. There is an algebra isomorph…

Let $M$ be a smooth projective variety endowed with a faithful action of a finite group $G$, and let $X:=M/G$ be its quotient. Assume that $X$ is Gorenstein, and let $Y\to X$ be an…

Let $M$ be a smooth projective holomorphic symplectic variety equipped with a faithful action of a finite group $G$ by symplectic automorphisms of $M$. If $Y$ is a symplectic resol…

Let $(W,G)$ be of Calabi–Yau type: $W$ is nondegenerate, not necessarily invertible, with weights $q_j$ satisfying … and $G$ contains $\langle j_W\rangle$ and lies in $SL_W$. Set…

Let $X$ and $Y$ be orbifolds related by an orbifold symplectic flop. The orbifold quantum cohomology rings are denoted by $QH^\ast_{CR}(X)$ and $QH^\ast_{CR}(Y)$. Ruan's conjecture…