Sentence:  3) Geometric interpretation of the <WSD>localization</WSD>./    Let "V" be an irreducible algebraic variety. Then "P" = "J"("V") is a prime ideal of \mathbb{C}[X_1, . . . , X_n] and so \mathbb{C}[V] = \mathbb{C}[X_1, . . . , X_n]/J(V) is an integral domain./    The <WSD>localization</WSD> \mathbb{C}[X_1, ...,X_n]_P is a subring of \mathbb{C}(X_1, ...,X_n) consisting of rational functions \{f/g : f,g \in \mathbb{C}[X_1, ...,X_n],g \notin P\} which are defined on a nonempty subset of "V". If "V" = {"x"} is a point, then "P" is maximal and \mathbb{C}[X_1, ...,X_n]_P = \{f/g : f, g \in \mathbb{C}[X_1, . . . , X_n], g(x) \ne 0\} consists of rational functions which are defined at "x". 
Meaning of the word marked with <WSD> tags:  A ring of fractions of a given ring, such that the complement of the set of allowed denominators is an ideal.