Computational Algebraic Geometry
Smoothness refers to a property of a geometric object where it has no singularities, meaning that it can be described by differentiable functions at every point. In algebraic geometry, smoothness indicates that the local structure of the variety behaves nicely, allowing for well-defined tangent spaces. This concept is crucial in understanding various algebraic constructs, as it ensures that methods applied to these objects, such as intersection theory or homotopy methods, are valid and effective.
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