Elementary Algebraic Geometry
Smoothness refers to a property of a space where it behaves nicely in terms of differentiability, meaning that it has no abrupt changes, singularities, or 'sharp points.' In algebraic geometry, smoothness implies that the variety is well-behaved at every point, allowing for the application of calculus and differential geometry concepts. This property is essential for understanding how varieties can be manipulated and transformed without encountering issues that arise from singular points.
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