26 problems

Let $\Gamma$ be a finite subgroup of $SL_2(\mathbb{C})$, let $\Gamma_n=\Gamma^n\rtimes S_n$, and let $X_{\Gamma,n}$ be the union of connected components of the $\Gamma$-fixed locus…

Let $V$ be a vector space, let $G\subset SL(V)$ be a finite subgroup, and set $X=V/G$. Assume that there is a proper smooth crepant resolution $\pi:Y\to X$. For each homomorphism…

Let $X=V/G$ be the quotient of a complex vector space $V$ by a finite subgroup $G\subset SL(V)$, and assume that $X$ admits a smooth crepant resolution $Y\to X$. Write…

Let $G$ be a finite subgroup of $\operatorname{SL}(r,\mathbb{C})$, let $X=\mathbb{C}^{r}/G$, and let $\widehat{X}\longrightarrow X$ be a crepant desingularization. For each integer…

Let $G\subset \operatorname{Sl}_n(\mathbb C)$ be a finite group, put $W=\mathbb C^n/G$, and let $X\rightarrow W$ be a crepant resolution. Write $D^b_G(\mathbb C^n)$ for the bounded…

Let $V$ be a vector space, let $G\subset SL(V)$ be a finite subgroup, and let $X\to V/G$ be a crepant resolution. Write $D^b_G(V)$ for the bounded derived category of $G$-equivaria…

Let $M$ be an algebraic symplectic manifold with a symplectic action of a finite group $G$, and let $X\to M/G$ be a smooth symplectic resolution. Choose deformation-quantizations…

Let $V$ be a symplectic vector space, let $G$ act symplectically on $V$, and let $X\to V/G$ be a symplectic resolution. The natural dilation action of $\mathbb C^*$ on $V$ lifts to…

Let $\Gamma$ be a finite subgroup of $SU(n)$, let $M=\mathbb{C}^n/\Gamma$, and let $\widetilde{M}$ be the crepant resolution introduced above. The relevant objects are the cohomolo…

Let $G$ be a finite subgroup of $\operatorname{SL}(d,\mathbb{C})$ such that $\mathbb{C}^d/G$ is minimally embeddable as a complete intersection in an affine space $\mathbb{C}^r$, w…

Tautological-sheaf basis conjecture. Under appropriate circumstances, the tautological sheaves $\mathcal F_\rho$ form a $\mathbb Z$-basis of $K_0(\operatorname{Coh}Y)$; their Chern…

Let $C_\zeta$ be the polyhedra associated with the parameter $\zeta$, let $n$ denote the ambient dimension, and let $\mathcal{S}^k$ be the configurations of codimension $k$ whose a…

Let $\Gamma\subset\operatorname{SU}(3)$ be an abelian group acting on $\mathbb{C}^3$ freely outside the origin. Let $X_0=\mathbb{C}^3/\Gamma$, and let…

Let $G\subset \operatorname{SL}(3,\mathbb{C})$ be a finite subgroup, let $Y={G}\operatorname{-Hilb}(\mathbb{C}^3)$ be the $G$-Hilbert scheme, and let … be the inverse of the Bridge…

Let $G\subset GL_2({\mathbb{C}})$ be any finite subgroup, and let $X$ be a resolution of $\mathbb{C}^2/G$. Let $Y$ be the maximal resolution of the pair $(\mathbb{C}^2/G,B)$, where…

Let $\Gamma$ be a finite subgroup of $SU(2)$, and let $X_\zeta$ be the space in the paper's theorem. Let $S_1,\ldots,S_r$ be the components of the $S^1$-fixed locus of $X_\zeta$ ge…

Let $G\subset\operatorname{GL}(2,\mathbb{C})$ be a finite subgroup, let $X=\mathbb{C}^2/G$ with boundary divisor $B$, and let $\mathcal{M}_{\theta}$ denote the moduli space of…

Wall-crossing conjecture. There is a path $\gamma\colon[0,1]\to\Theta(Q_G,\ub{d})$ passing through walls $\mathfrak{w}_1,\dots,\mathfrak{w}_m$ satisfying the conditions in the wall…

Let $X$ be a scheme of dimension at least $2$, let $K,L$ be line bundles on $X$, and let $p_i:X^n\to X$ be the projections. Set … Let $\rho:X^{[n]}\to X^{(n)}$ be the Hilbert–Chow…

Let $X$ be a smooth projective scheme, let $X^{(n)}=X^n/\mathfrak{S}_n$ be its $n$th symmetric product, and let … be the Hilbert–Chow morphism. K-theoretic McKay conjecture. The K-…

Let $k$ be a perfect field of characteristic $p>0$, let $G=\alpha_p$, and let $V$ be a finite-dimensional representation of $G$ with quotient $V/G$. Let $H=\mathbb{Z}/p\mathbb{Z}$…

Let $H$ be a semisimple Hopf algebra and let $A$ be a noetherian Artin–Schelter regular, connected graded algebra generated in degree one. Suppose that $A$ is a graded $H$-module a…

Let $V$ be a smooth quasi-projective variety, and let $G$ be a finite subgroup of $\operatorname{Aut}(V)$ such that $\omega_V$ is $G$-equivariantly locally trivial. Let $Z\to V/G$…

Let $G$ be a finite subgroup of $SU(2)$, let $\widehat{\mathbb{C}^{2}/G}$ be the crepant resolution of $\mathbb{C}^{2}/G$, and let $[\mathbb{C}^{2}/G]$ be the corresponding orbifol…

Let $G\subset SO(3)$ be a polyhedral subgroup, let $\mathcal{X}=[\mathbb{C}^{3}/G]$, and let $F_{0}^{\mathcal{X}}(x_1,\ldots,x_n)$ denote its $\mathbb{C}^{*}$-equivariant genus-zer…