5 problems

Birkar's conjecture. The Stein degree

Let $d\in\mathbb{N}$ and let $t\in\mathbb{R}^{>0}$. Let $(X, B)\to Z$ be a log Calabi-Yau fibration of dimension $d = \dim X$, and let $S$ be a horizontal$/Z$ irreducible component…

Let $d$ be a positive integer and $\epsilon$ a positive real number. Let $(X,B+\mathbf{M})$ be a generalized pair of dimension $d$ and let $\pi:X\to Z$ be a contraction between pro…

Let $d$ be a positive integer and $\tau$ a positive real number. A log pair $(X,B)$ of dimension $d$ and a contraction $\pi:X\to Z$ between projective normal varieties are assumed…

Let $d$ be a natural number and let $\epsilon$ be a positive real number. Consider a generalised pair with data $X'\to X\overset{f}\to Z$ and $M'$, where $f$ is a contraction. The…