10 problems

Let $T(Y,\overline{Y},\widetilde{Y})$ be a geometric transition satisfying a good condition, for example that its birational morphism $\phi$ contracts $k$ exceptional divisors to a…

Let $T(Y,\overline{Y},\widetilde{Y})$ be a geometric transition, and let $Y^{\circ}$ and $\widetilde{Y}^{\circ}$ be mirror partners of $Y$ and $\widetilde{Y}$, respectively. Morris…

Let $Y$ be a smooth complete variety with toric degeneration $Y_0$, let $Y_0^\vee$ be its $f$-mirror partner, and suppose there is a geometric transition … Let $k_Z$ and $m_Z$ deno…

Let $Y$ be a smooth complete algebraic variety that is the generic fiber of a flat family with special fiber $Y_0$, where $Y_0$ is a complete intersection in a complete toric varie…

Let $\widehat{X}$ and $\widetilde{X}$ be Calabi--Yau manifolds, and suppose they are related by a geometric transition … where $\widehat{X} \dashrightarrow X$ is a birational contr…

Consider the graph whose nodes are deformation classes of simply connected Calabi–Yau threefolds and whose edges are given by geometric transitions. Call a node primitive if its de…

Direct connectedness conjecture. If $\mathcal{M}_1$ and $\mathcal{M}_2$ are nodes of the Calabi–Yau web with distinct Picard numbers $\rho_1>\rho_2$, then there exists a unique arr…

Small-transition decomposition conjecture. Every small geometric transition which does not admit any conifold degeneration is equivalent to a composition of conifold transitions. C…

A geometric transition is abbreviated g.t.; a geometric transition is small and rigid when it has those properties. A factorization of a geometric transition $T$ is an expression ……

Type I conifold-degeneration conjecture. Every type I geometric transition admits a conifold degeneration. In particular, the canonical model of a type I geometric transition is a…