algebraic variety

An algebraic variety is a collection of points that satisfy a specific set of polynomial equations. Think of it as a geometric shape defined by mathematical relationships. For example, the curve of a circle or a parabola can be described by such equations. These varieties serve as fundamental objects in algebraic geometry, a branch of mathematics exploring the connections between algebra (like equations) and geometry (shapes and spaces). They can be one-dimensional (like curves) or higher-dimensional (like surfaces), playing a crucial role in various fields, including physics and data science.