A Fano variety is a special type of algebraic variety in mathematics, particularly in the field of algebraic geometry. It is characterized by having positive first Chern class, which implies that it has ample line bundles. Fano varieties are important because they often exhibit nice geometric properties and can be used to study more complex varieties. These varieties can be classified into different types based on their dimensions and other features. Examples of Fano varieties include projective spaces and certain hypersurfaces. They play a significant role in various areas of mathematics, including mirror symmetry and string theory.