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A surface is a generalization of a plane which needs not be flat, that is, the curvature is not necessarily zero. This is analogous to a curve generalizing a straight line
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Divisorial contraction: when is the image an algebraic space or a stack?
In order to have a contraction morphism $X\to Y$, the intersection matrix must be negative definite.
Conversely, if the intersection matrix is negative definite, the contraction morphism exists in th …