7 problems

A degenerate singular fiber is a fiber associated with a degenerate singularity of an integrable system. Isotropic-fiber conjecture. In most cases, degenerate singular fibers shoul…

Let $f\colon \mathcal{X}\to S$ be a family of Calabi–Yau manifolds with a semi-stable singular fiber $X_0=f^{-1}(0)$. Let $a_0$ be the coefficient of the Dirac current in the curre…

Tan–Tu conjecture. Every semistable non-isotrivial fibered surface $f:X\to \mathbb{P}^1$ of general type has at least $7$ singular fibers.

Let $mF$ be a multiple fiber of a smooth $\mathbb A^1$-fiber space with irreducible fibers. Let $k$ be the coefficient of $F$ in the canonical divisor $K_X$. Define a rational numb…

Conjectured codimension-three enhancement. Over $\Pi_3$ and $\Pi_4$, respectively, the fiber enhances to an $I^*_2$ fiber and an $IV^*$ fiber; more generally, the fibers have dual…

Conjectured fiber-enhancement pattern. The $I_5$ fiber enhances to an $I_6$ fiber over $\Sigma_{5}$ and to an $I^*_1$ fiber over $\Sigma_{10}$:

Joyce's singular-fiber conjecture. The discriminant locus has codimension one and is locally contained, in affine coordinates, in the plane corresponding to the monodromy-invariant…