3 problems

Let $X$ be a klt variety, let $x \in X$ be a closed point, and let $\mathfrak{m}_x$ denote the maximal ideal corresponding to $x$. Ideal-adic semi-continuity conjecture. For every…

Let $X$ be a klt variety and let $x\in X$ be a point defined by the ideal $\mathfrak{m}_x$. For an $\mathbf{R}$-ideal $\mathfrak{a}=\prod_{j=1}^r\mathfrak{a}_j^{\lambda_j}$, let…

Let $(X,\Delta)$ be a pair, meaning that $X$ is a normal variety and $\Delta$ is an effective $\mathbb{R}$-divisor with $K_X+\Delta$ an $\mathbb{R}$-Cartier divisor. Let $Z$ be a c…