7 problems

Let $(\overline{\mathscr{S}}_{K}^{\Sigma}(G,X),\mathcal{M}_{\overline{\mathscr{S}}_{K}^{\Sigma}(G,X)})$ be the special fiber of the toroidal compactification of the Shimura variety…

Let $\mathcal{M}$ be a moduli algebraic stack of polarized log-terminal Calabi–Yau varieties with quasi-projective coarse moduli variety $M$. A weak K-moduli stack is a proper Deli…

Let $\overline{\mathscr{B}}$ be the stable pairs compactification of the space of elliptic K3 surfaces, parametrizing pairs $(X,\epsilon S+\delta F)$ for sufficiently small positiv…

Let … lambda{2i+1}$and the classes of boundary strata, and no polynomial in the$Dm$, is identically zero for$g$ sufficiently large. This predicts algebraic independence of the i…

Let ${{\mathcal A}_{g,\operatorname{smooth}}^{\operatorname{Perf}}}$ denote the smooth locus of the perfect cone toroidal compactification, and let…

Let $\mathbf{X}$ be pure $p$-integral Shimura data. Let any embedding ${}^K_\Delta \mathbf{X} \hookrightarrow {}^{K'}_{\Delta'} \mathbf{X}'$ in a datum of symplectic type…

Vanishing conjecture. The intersection numbers $a_N^{(g)}$ for any $N$ vanish unless $G-N=k(k+1)/2$ for some $k\le g$. The claim extends the vanishing pattern established in the pa…