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>生成点（英語版）(generic point)
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Generic point
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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).
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