17 problems

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…

Consider the toric-degeneration setup in which a smooth Calabi–Yau variety $Y$ has a geometric transition $T(\widehat{Y},\overline{Y},Y)$ induced by a small toric degeneration, and…

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…

The families consist of the Spin(7) holonomy metrics $(M_{S^5},\Psi_{\mu})$ and $(M_{\mathbb{C}P^{2}},\Upsilon_{\tau})$, whose AC members are asymptotic to the same Spin(7) cone. T…

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…

Calabi–Yau Web Conjecture. More or less all Calabi–Yau threefolds can be connected to each other by means of a chain of geometric transitions.

Let $C_k$ be the Lagrangian submanifold in the resolved geometry that specifies boundary conditions for open strings, and let $S_{\mathrm{eff}}$ be the deformed Chern–Simons action…

A Calabi–Yau threefold is a smooth projective threefold $X$ with trivial canonical divisor and vanishing cohomology … A geometric transition is a degeneration of a Calabi–Yau three…

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…

Calabi–Yau web connectedness conjecture. Calabi–Yau threefolds can be arranged in a giant connected web whose nodes are deformation classes and whose arrows are induced by geometri…

Calabi–Yau Web Conjecture. All Calabi–Yau threefolds can be connected to each other by a chain of geometric transitions.

Let the compact geometry have sixteen nodes locally modeled on conifolds, with RR-flux through an $mathcal A_i$-cycle and RR-flux through the $mathcal B$-cycle. Consider fluxes who…