125 problems

Let $\pi:\mathcal{X}\rightarrow\Delta$ be a smoothing of a Kähler–Einstein orbifold $(X_0,\omega_0)$ with $A_k$-singularities, and suppose that $\operatorname{Aut}(X_0)$ is discret…

Global period-index conjecture. For any such Brauer class $\alpha$,

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 $\mathcal{M}$ 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…

Let $(Y/\boldsymbol{\Delta})$ be a smooth projective Campana constellation supported by a firmament $\boldsymbol{\Gamma}$. Campana's conjecture. Points on $Y$ integral with respect…

Let $\mathcal{X}$ be an orbifold satisfying the hard Lefschetz condition and admitting a crepant resolution $Y$. Let $F^Y$ and $F^\mathcal{X}$ denote their potential functions, wit…

Formality conjecture. The Hochschild complex of the algebra $C^\infty(M)\rtimes G$ is a formal differential graded Lie algebra.

For $g\geq 2$, let $\M_g$ be the moduli orbifold of genus-$g$ Riemann surfaces. Nonpositive-curvature conjecture. The orbifold $\M_g$ admits no complete, finite-volume Riemannian m…

For $g\geq 3$, let $\M_g$ be the smooth moduli orbifold of genus-$g$ Riemann surfaces. Maximality conjecture for $\M_g$. The orbifold $\M_g$ does not finitely orbifold-cover any ot…

Let $n\leq 16$, and let $\mathcal{O}$ be an elliptic $n$-orbifold. Write $V_{c}(\mathcal{O})$ for its conformal volume. Uniform conformal-volume conjecture. There is a function…

Let $G$ be a finite group, or more generally a linear algebraic group, acting on a variety $X$, and let $X\to Y:=X/G$ be the quotient. A $G$-variety is a variety with a $G$-action,…

Let $\mathcal A$ be a chiral conformal net with a finite gauge-group action by $\Gamma$, and let $\mathcal A^\Gamma$ denote its fixed-point orbifold net. Consider the irreducible D…

Degenerate Frobenius structure conjecture. There is a degenerate $G$-Frobenius algebra of degree $j$ on the dual of a $G$-Euler $G$-Frobenius algebra.

Let $Y^\partial$ be a smooth or e-admissible effective orbifold, let $g^\partial:Y^\partial\rightarrow Z$ be a fibration, and let $Y_z^\partial$ be its orbifold general fiber. Orbi…

Let $X^\partial$ be a smooth projective effective orbifold with $\kappa(X^\partial)=-\infty$. An orbifold Mori fibration is a fibration whose general fibers are orbifold rationally…

Let $f:X\to C$ be a fibration over a function field, with $K$-core factorization $f=g_f\circ c_f$ and base orbifold $(C(f)/\Delta(c(f)))$. Conjecture III{FF}. The $K'$-rational poi…

Let $c_X:X\to C(X)$ be an admissible representative of the core of $X$, and let $\Delta(c_X)$ be its base orbifold. Conjecture IV'H. One should have … In addition, if $(X/\Delta)$…

Let $f:X\dashrightarrow Y$ be a special fibration with $\kappa(Y,f)=-\infty$. Let $\Delta(f)$ be its base orbifold, and let $\kappa$-rationally generated mean that the general orbi…

Let $g:(Y/H)\to Z$ be a prepared and high holomorphic fibration between manifolds, with $Y\in\mathcal C$. Let $\Delta(g,H)$ be its base orbifold, let $z\in Z$ be general, and write…

Let ${\mathfrak{e}}_{10}$ be the hyperbolic Kac–Moody algebra, and let $\mathcal{U}_{2}^{{\mathbbm{Z}}_{n}}$ be the automorphism defining the orbifold action. Let…

Physicists' Euler number conjecture. In appropriate circumstances,

Orbifold rationality conjecture. The conformal subalgebra $V^G$ is also strongly rational.

Compact orbifold uniqueness conjecture. The unitary $V^G$-module $V$ has a unique unitary VOA structure up to isomorphism.