8 problems

DT/PT $\mathbb{Z}_{n}$-orbifold vertex correspondence. If $\nu$ is multi-regular, then

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

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

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…