3 problems

Invariance of plurigenera conjecture. For every $m$, the quantity $P_m(X_t)$ is independent of $t\in B$. The claim predicts deformation invariance of these dimensions in smooth fam…

Sun–Zhang's conjecture. A polarized Fano fibration $(\pi:X\to Y,\xi)$ admits a Kähler–Ricci shrinker $(\omega,\xi)$, unique up to automorphisms of $X$ preserving $\xi$, if and only…

Let $X$ be a polarized variety with polarization $L_X$, and let $D$ be a divisor. A metric on $X\setminus D$ is said to be of Poincaré type when it has the prescribed Poincaré asym…