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Let $X$ be a normal scheme and $|D|$ a linear system on $X$. In "Singularity of Minimal Model Program" by Janos kollar p249, it says, If $X$ is a variety over $\mathbb{C}$, and $E_j$ ...

A normal singularity $(X,x)$ over a field $k$ is terminal (resp. canonical) if $(i)$ it it is $\mathbb{Q}$-Gorenstein. and $(ii)$For any resolution of singularity $F:Y\rightarrow X$, $K_Y-f^*K_X>...

Let $(R,\mathfrak{m })$ be a three dimensional complete local ring over a field $k$ of arbitrary characteristic and let $f\in R$ and $R/f$ is a rational double point. My question is as follows. Are ...

M. Reid defines cDV singularity as follow in his paper "CANONICAL 3-FOLDS" A point $p\in X$ of a 3-fold is called a compound Du Val point if for some section H throgh $P$, $P\in H$ is a Du ...