4 problems

Let $f:(U_X,X)\rightarrow (U_Y,Y)$ be a proper, not necessarily birational, morphism between nonsingular toroidal embeddings such that … and such that $f|_{U_X}:U_X\rightarrow U_Y$…

Toroidal lifting conjecture. There exist modifications $X'\to X$ and $B'\to B$, each a composition of blowings up with smooth centers lying over $\Sigma$, and a lifting $X'\to B'$…

Let ${\cal M}$ be a moduli space of complex structures on an $n$-dimensional Calabi–Yau variety $W$, and let ${\cal M}'$ be a moduli space for a mirror Calabi–Yau variety $W'$. Let…

Let $X$ and $Y$ be nonsingular varieties over an algebraically closed field of characteristic $0$, and let $f:X\longrightarrow Y$ be a dominant morphism. Let $D_Y$ be a simple norm…