In mathematics, a Fano space is a type of algebraic variety that is characterized by having a specific geometric structure. It is a projective variety that satisfies certain conditions, making it a fundamental object of study in algebraic geometry. Fano varieties are known for their positive curvature properties, which often lead to interesting results in both geometry and topology. A Fano manifold is a particular case of a Fano space, where the variety is also a smooth manifold. These manifolds play a crucial role in the classification of algebraic varieties and have applications in various areas of mathematics, including string theory and mirror symmetry. Their unique properties make them a central topic in modern mathematical research.