In set theory, a subset of a Cartesian product of two sets is called a binary relation or correspondence; thus, a correspondence here is a relation that is defined by algebraic equations.
There are some important examples, even when V and W are algebraic curves: for example the Hecke operators of modular form theory may be considered as correspondences of modular curves.
However, the definition of a correspondence in algebraic geometry is not completely standard.
For instance, Fulton, in his book on intersection theory,[1] uses the definition above.
Correspondences also play an important role in the construction of motives (cf.