A Fano variety is a special type of algebraic variety in mathematics, particularly in the field of algebraic geometry. It is defined as a projective variety that has a positive first Chern class, which means it has certain geometric properties that make it interesting to study. Fano varieties are often used to understand more complex varieties and can be classified based on their dimensions and other characteristics. One of the key features of Fano varieties is that they have ample anticanonical bundles. This property allows for the existence of many rational curves on the variety, making them rich in structure. Fano varieties play a significant role in various areas of mathematics, including mirror symmetry and string theory.