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A surface is a two-dimensional topological manifold. The term can also be used to describe a smooth surface, depending on the context.

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The exceptional locus of a minimal resolution of singularities

Let X be a surface. (A surface is an excellent integral normal separated 2-dimensional scheme.) Let $\psi:Y\longrightarrow X$ be a minimal resolution of singularities and let $E$ be an irreducible co …