Smooth Varieties

Smooth varieties are a concept in mathematics, particularly in algebraic geometry. They refer to certain shapes or geometric objects defined by polynomial equations, where every point on the shape is well-defined without any sharp edges or singular points. Essentially, a variety is considered smooth if you can smoothly move along its surface without encountering any breaks or abrupt changes in direction. This property makes smooth varieties easier to study and understand, as they possess nice mathematical characteristics, allowing for the application of various mathematical techniques in analysis and computations.