327 problems

A stratum of translation surfaces is a quasi-projective variety, and its orbifold fundamental group is finitely presented. A connected component of a stratum is a classifying space…

Let $\mathcal{X}$ be a hard-Lefschetz Gorenstein orbifold and let $Y$ be its crepant resolution. Let the GW potentials encode the Gromov–Witten theories of $\mathcal{X}$ and $Y$. B…

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

Let $V$ be a vertex operator algebra, let $G\leq\operatorname{Aut}(V)$ be a finite group, and let … be the fixed-point subalgebra. Assume that $V$ is $C_2$-cofinite and rational. O…

Let $S$ be a connected $2$-manifold without boundary, and let a discrete group $G$ act on $S$ effectively, properly discontinuously, and with isolated fixed points. Assume that…

Mondino's conjecture. $(X,\mathsf{d})$ is homeomorphic to an orbifold, possibly with boundary.

Let $(f,G\rtimes S)$ and $(\widetilde{f},\widetilde{G}\rtimes S)$ be BHHT-dual pairs, where the permutation group $S$ satisfies the parity condition (PC). Let…

Dijkgraaf–Moore–Verlinde–Verlinde conjecture.

Let ${\mathcal H}(n)$ be the rank-$n$ Heisenberg vertex algebra, with orthogonal-group orbifold ${\mathcal H}(n)^{\operatorname{O}(n)}$. Its generators have a first relation at wei…

Let $\Gamma$ be the orbifold fundamental group of a compact good orbifold, acting on its universal orbifold cover $\widetilde{M}$, and let $H_V=\Delta+V$ be a $\Gamma$-invariant Sc…

Let $M$ be a hyperbolic knot complement in $\mathbb{S}^3$ with hidden symmetries. A cusp of an orbifold is a $(2,3,6)$-cusp when its cross-section is the Euclidean triangle orbifol…

Let $(X,\Delta)$ be a smooth proper orbifold curve over a number field $K$, where $\Delta=\sum_i(1-\frac{1}{m_i})D_i$, and call $(X,\Delta)$ Mordellic if, after every finite field…

Let $M$ be a connected aspherical $2$-dimensional orbifold, meaning that its universal orbifold cover $\widetilde M$ is a contractible orbifold, equivalently that…

Let $M$ be a connected orbifold, and let $f(M)$ denote the homomorphism between Lie groupoids associated with the configuration-space construction. A homomorphism of Lie groupoids…

Donaldson–Thomas crepant resolution conjecture. One has

Let $G$ be a finite group and let $\pi:\mathcal{Y}\to\mathcal{B}$ be a $G$-gerbe over a smooth Deligne–Mumford stack with trivial generic stabilizer. Let…

Flexibility conjecture. These types of real projective orbifolds with R-ends might be very flexible.

Let $\mathcal{Z}$ be a hard-Lefschetz $3$-orbifold, and let … be a crepant resolution. Let $DT_{mr}(-)$ denote the reduced, multi-regular Donaldson–Thomas potential, and let…

Orbifold Green–Griffiths–Lang conjecture. If $\mathcal{X}$ is of general type, then there exists a proper sub-orbifold $\mathcal{Z}\subset\mathcal{X}$ containing the image of every…

A Kleinian group is a discrete subgroup of the group of isometries of hyperbolic $3$-space, and its co-volume is the hyperbolic volume of the corresponding quotient orbifold. Let…

Let $X$ be a smooth quasi-projective surface, let $G$ act on $X$, and suppose there is a smooth resolution $\widetilde{X/G}$ of the orbifold $X/G$ such that…

Dixon–Harvey–Vafa–Witten conjecture. The Euler characteristic of $Y$ should satisfy

Let $\mathcal{M}$ be the subcategory of $C^n$-manifolds, where $n\in\mathbb{N}$ or $n=\infty$, consisting of all manifolds but only diffuse $C^n$-functions. Let the elementary fini…

Let $S$ be an infinite set, and let $f$ be a $\text{\bf Gen}[S]$-morphism, where $\text{\bf Gen}[S]$ is the subcategory of objects admitting a cover by open sets of cardinality at…

Let $\text{\bf Gen}$ be the category of topological spaces under consideration, equipped with its pseudoétale and torsorial topologies. The formal smallness conjecture. The pseudoé…