6 problems

Let $W$ be the coarse projective variety in the KSBA moduli problem, let ${\mathfrak W}\to W$ be a $\mu_N$-gerbe, and let $M$ be the associated KSBA moduli space. Suppose that the…

Let $M_N$ be a KSBA moduli space of surfaces of general type, and consider the Miller–Morita–Mumford classes, also called characteristic classes, of the diffeomorphism group of gen…

Let $M_N$ be the KSBA moduli stack of index one covers, let $M_N^{\operatorname{Bub}}$ be the moduli stack of bubble-tree index one cover DM stacks, and let…

A maximal log Calabi–Yau variety is a projective variety paired with a boundary divisor whose log canonical class is trivial and whose boundary has maximal combinatorial complexity…

Semiampleness conjecture. The generalized Hodge line bundle $\lambda$ is semiample.

Wormhole conjecture. The MMP requires only flips and gives a minimal model. The KSBA replacement of $(X'\subset\mathcal{X}')\to(0\in\mathbb{D})$ lives on the same moduli space as t…