A projective curve is a type of geometric object that arises in the study of algebraic geometry. It can be defined as the set of solutions to a polynomial equation in projective space, which is a way of extending the concept of Euclidean space to include points at infinity. This allows for a more comprehensive understanding of curves, as it captures their behavior at these infinite points. In projective geometry, points are represented using homogeneous coordinates, which helps in analyzing properties that remain invariant under transformations. Projective curves can be classified based on their degree, and they play a crucial role in various mathematical fields, including algebraic geometry and number theory.