Algebraic varieties are the fundamental objects of study in algebraic geometry, defined as the solution sets of polynomial equations over a given field. These geometric structures can be understood in various dimensions and can exhibit complex behaviors, such as singularities and intersections, which are essential for understanding their properties. They serve as a bridge between algebra and geometry, providing tools to analyze their shape, dimension, and other important characteristics in different contexts.
congrats on reading the definition of Algebraic Varieties. now let's actually learn it.