14 problems

Crepant resolution conjecture. The transformation $\mathds{T}$ satisfies

Let $\mathcal{X}$ be an orbifold with projective coarse moduli space $X$, and let $\pi:Y\to X$ be a crepant resolution. Suppose that the big quantum products $\bullet_\tau$ for…

Let $\mathcal{X}$ be an orbifold with projective coarse moduli space $X$, and let $Y$ be a crepant resolution. Consider the quantum cohomology Frobenius manifolds associated to…

Suppose that $\mathcal{X}$ is an orbifold with projective coarse moduli space $X$, and that $Y$ is a crepant resolution of $X$. Let…

Let $r$ be a positive integer, let $[[200~\mathbb C^4/\mathbb Z_r]$ be the quotient Calabi–Yau $4$-orbifold considered in the source, and let $q_0,\ldots,q_{r-1}$ be variables. Wri…

Let $G=\mathbb{Z}_r<\mathrm{SU}(2)<\mathrm{SU}(4)$ or $G=\mathbb{Z}_2\times\mathbb{Z}_2<\mathrm{SO}(3)<\mathrm{SU}(4)$. Let $X\to\mathbb{C}^4/G$ be the Nakamura $G$-Hilbert crepant…

Let $Y$ be the local resolution and let $\mathcal{X}$ be the corresponding orbifold, with genus-zero free energies $F_Y^0$ and $F_{\mathcal{X}}^0$. Their differentials define graph…

Let $S$ be a surface, and let $\operatorname{Hilb}^k S$ and $\operatorname{Sym}^k S$ denote its Hilbert scheme and symmetric product. Crepant resolution conjecture. The quantum coh…

Let $\mathcal{G}$ be an ADE Lie group with Cartan torus $\mathcal{T}$, let $Q_i$ be exponentiated linear coordinates on $\mathcal{T}$, and let $l_i$ be the $i$th component of the h…

Let $\mathcal{X}\rightarrow X\leftarrow Y$ be toric Calabi--Yau threefolds satisfying the closed crepant resolution conjecture, let…

Let $\mathcal{X}$ be a smooth Deligne--Mumford stack and $Y$ a crepant resolution, and let $\mathbb{U}_{K,\rho}^{\mathcal{X},Y}:K(Y)\to K(\mathcal{X})$ denote the isomorphism of…

Let $\mathcal{X}$ be a toric Gorenstein orbifold and $Y$ a crepant resolution, with Givental spaces … for $\mathcal{Z}=\mathcal{X},Y$, equipped with the symplectic form…

Let $\mathcal{X}$ be a toric Gorenstein orbifold, and let $X \leftarrow Y$ be a crepant resolution of its coarse moduli space. A global quantum $D$-module is a tuple…

Let $\mathcal{A}_r$ be the type-$A_r$ surface, let $\operatorname{Hilb}^n(\mathcal{A}_r)$ be its Hilbert scheme of $n$ points, and let $L$ be the map defined in Section 5. Consider…