8 problems

Let $Y$ be a Calabi–Yau threefold with a fibration structure. A Tyurin degeneration is a degeneration of another Calabi–Yau threefold into normal crossing (quasi-)Fano components,…

Let $X$ be a Calabi–Yau $3$-fold with a Lefschetz K3-fibration $\pi:X\rightarrow Y$, and let a gradient cycle be a graph in $Y$ whose edges are decorated by $2$-cycles in the K3 fi…

Type (1) face orbit conjecture. The pseudoautomorphism group $\operatorname{PsAut}(Y)$ acts with finitely many orbits on the Type (1) faces of $\operatorname{Mov}^{e}(Y)$ for every…

Twisted K3-fibration finite-generation conjecture. One has

K3-fibration finite-generation conjecture. For $\gamma\in H_2(B,\mathbb Z)$,

Let $W$ be a Calabi–Yau threefold mirror to a degenerating Calabi–Yau threefold, and let $D=\sum_{i=1}^n a_iD_i$ be the divisor on $W$ corresponding under mirror symmetry to the mo…

Let $V$ be a nonsingular projective threefold that is the total space of a K3 fibration $\pi:V\to C$ over a nonsingular projective curve, and let $\beta\in H_2(V,\mathbb{Z})^\pi$ b…

Perverse stable-pair partition-function conjecture. The partition functions satisfy