14 problems

Let $X$ be a complex manifold equipped with an effective action of a finite group $G$. Write $X/G$ for the quotient, and let $\widehat{Ell}(X/G,;y,q)$ denote the normalized ellipti…

DCC conjecture. The set of volumes of these orbifold pairs satisfies the descending chain condition, and its minimum nonzero value is

DCC conjecture. The set of volumes of such orbifold pairs satisfies the descending chain condition, and its minimum nonzero value is

Characterization of torus quotient pairs. In the above setting, the following are equivalent: 1. $\mathrm{c}_{1}(K_X+\Delta)=0\in \HH2.X.{\mathbb{R}}.$ and

Greb–Kebekus conjecture. 1. $\mathrm{c}_{1}(X)=0\in \HH2.X.{\mathbb{R}}.$, and there exists a Kähler class $\alpha\in \HH2.X.{\mathbb{R}}.$ such that

Let $H_{g,n}(x_1,\dots,x_n)$ be the $n$-point generating function for connected $q$-orbifold monotone Hurwitz numbers, and consider the spectral curve … Let…

The remodeling conjecture. The open-closed Gromov–Witten potentials satisfy the displayed identities relating them to the topological-recursion invariants, including the stable cas…

Orbifold fundamental group conjecture. The group $\pi_1(X,D)$ is almost abelian, finite if $(X,D)$ is klt, and trivial if $(X,D)$ is purely logarithmic or if…

Orbifold rational curves conjecture. 1. $(X,D)$ is uniruled if and only if $K_X+D$ is not pseudo-effective. 1'. $(X,D)$ is uniruled if and only if it is weakly uniruled. 2. $(X,D)$…

In the effective case $|G_0|=1$, let $g_1=i_0$ and consider the matrix … The non-negativity conjecture. The entries of the inverse of the above matrix are non-negative integers. Th…

Let $G_s$ be the index set used for the orbifold vertex, let $q_0$ and $q_g$ be its closed and open variables, and let $b_{hg}$ be the coefficients defined by the inverse matrix re…

The stability conditions and Frobenius structures conjecture. The following should hold: (i) $M_A$ is isomorphic to…

Let $G$ be a finite group acting on ${\bf C}^n$, and suppose that ${\bf C}^n/G$ admits a crepant resolution. The orbifold Euler characteristic conjecture. The orbifold Euler number…

Let ${\mathcal X}$ be a smooth Gorenstein Deligne–Mumford stack over $F_q$, with coarse moduli space $X=|{\mathcal X}|$, and suppose there is a crepant resolution $\pi:Y\to X$. Ass…