8 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 $X_0$ be a conifold degeneration of a generic Calabi–Yau complete intersection $X\subset G(k,n)$, let $p$ be the number of nodes of $X_0$, and set $\alpha=(k-1)(n-k-1)$. Let…

Consider the directed graph whose nodes are deformation families of smooth, compact Calabi-Yau threefolds. For two nodes $\mathcal{M}_1$ and $\mathcal{M}_2$, draw an arrow … when,…

Let $chat{X}$ be a Calabi–Yau threefold, and let … be a conifold transition. Let $(\Omega_t,\omega_t,h_t)$ denote the holomorphic volume form, Hermitian form, and bundle metric inv…

Related-nodes conjecture. A set of nodes $p_1,\ldots,p_k$ in $(B,\mathcal P,\phi)$ can be simultaneously resolved by the above process if and only if they are related.

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…