Abstract configurations in algebraic geometry

TL;DR

This paper explores abstract configurations, especially finite geometries, within algebraic geometry, highlighting their structures and providing examples to deepen understanding of their properties.

Contribution

It introduces and discusses specific examples of abstract configurations and finite geometries relevant to algebraic geometry, expanding the understanding of their structures.

Findings

Examples of abstract configurations are provided.

Finite geometries are analyzed within algebraic geometry.

Insights into the structure of configurations are discussed.

Abstract

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.