https://en.wikipedia.org/wiki/Generic_point Generic point (抜粋) In algebraic geometry, a generic point P of an algebraic variety X is, roughly speaking, a point at which all generic properties are true, a generic property being a property which is true for almost every point.
In scheme theory, the spectrum of an integral domain has a unique generic point, which is the minimal prime ideal.
Contents 1 Definition and motivation 2 Examples 3 History
History
In the foundational approach of Andre Weil, developed in his Foundations of Algebraic Geometry, generic points played an important role, but were handled in a different manner. For an algebraic variety V over a field K, generic points of V were a whole class of points of V taking values in a universal domain Ω, an algebraically closed field containing K but also an infinite supply of fresh indeterminates. This approach worked, without any need to deal directly with the topology of V (K-Zariski topology, that is), because the specializations could all be discussed at the field level (as in the valuation theory approach to algebraic geometry, popular in the 1930s).
