7 problems

Support-space conjecture. The morphism $\Sigma\rightarrow S$ is a disjoint union of locally closed immersions.

Let $d$ be a positive integer and let $\Gamma\subset [0,1]$ be a DCC set of real numbers. A $\Gamma$-base-point-free $b$-divisor $\mathbf{D}$ on a normal projective variety $X$ is…

Let $d$ be a positive integer and let $\Gamma_0$ be a finite set of rational numbers. An lc-trivial fibration is a fibration $f:(X,B)\rightarrow Z$ with the usual lc-triviality con…

Let $G$ be a complex reductive group with maximal compact subgroup $K$, let $V$ be a finite-dimensional $G$-representation, and let $x\in V$ be semistable. Let $p_x$ be the associa…

The iterated balanced filtration is a canonical sequential filtration associated to a point of a noetherian algebraic stack with affine diagonal that admits a good moduli space and…

Let $X$ be a projective $K(\pi,1)$, meaning a projective variety whose universal cover is contractible, and let $\sigma\in\operatorname{Aut}(\mathbb{C})$. Write $X^\sigma$ for the…

Local freeness conjecture for weakly semistable morphisms. The sheaf