Abstract configurations in algebraic geometry

An abstract $(v_k,b_r)$-configuration is a pair of finite sets of cardinalities $v$ and $b$ with a relation on the product of the sets such that each element of the first set is related to the same number $k$ of elements from the second set and each element of the second set is related to the same number $r$ of elements in the first set. An example of an abstract configuration is a finite geometry. In this paper we discuss some examples of abstract configurations and, in particular finite geometries, which one encounters in algebraic geometry.