du Val singularity

du Val singularies are classified by the simply laced Dynkin diagrams, a form of ADE classification.

In algebraic geometry, a du Val singularity, also called simple surface singularity, Kleinian singularity, or rational double point, is an isolated singularity of a complex surface which is modeled on a double branched cover of the plane, with minimal resolution obtained by replacing the singular point with a tree of smooth rational curves, with intersection pattern dual to a Dynkin diagram of A-D-E singularity type. They are the canonical singularities (or, equivalently, rational Gorenstein singularities) in dimension 2. They were studied by Patrickdu Val (1934a, 1934b, 1934c) and Felix Klein.

单词	Simple singularity
释义	Simple singularity 英语百科 du Val singularity In algebraic geometry, a du Val singularity, also called simple surface singularity, Kleinian singularity, or rational double point, is an isolated singularity of a complex surface which is modeled on a double branched cover of the plane, with minimal resolution obtained by replacing the singular point with a tree of smooth rational curves, with intersection pattern dual to a Dynkin diagram of A-D-E singularity type. They are the canonical singularities (or, equivalently, rational Gorenstein singularities) in dimension 2. They were studied by Patrickdu Val (1934a, 1934b, 1934c) and Felix Klein.
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Simple singularity

du Val singularity