. "In algebraic geometry, a geometric quotient of an algebraic variety X with the action of an algebraic group G is a morphism of varieties such that (i) For each y in Y, the fiber is an orbit of G.(ii) The topology of Y is the quotient topology: a subset is open if and only if is open.(iii) For any open subset , is an isomorphism. (Here, k is the base field.) The notion appears in geometric invariant theory. (i), (ii) say that Y is an orbit space of X in topology. (iii) may also be phrased as an isomorphism of sheaves . In particular, if X is irreducible, then so is Y and : rational functions on Y may be viewed as invariant rational functions on X (i.e., of X). For example, if H is a closed subgroup of G, then is a geometric quotient. A GIT quotient may or may not be a geometric quotient: but both are categorical quotients, which is unique; in other words, one cannot have both types of quotients (without them being the same)."@en . "Inom algebraisk geometri, en del av matematiken, \u00E4r ett geometriskt kvot av en algebraisk varietet X med verkan av en G en s\u00E5 att (i) F\u00F6r varje y i Y \u00E4r fibern en bana av G.(ii) Topologin av Y \u00E4r : en delm\u00E4ngd \u00E4r \u00F6ppen om och bara om \u00E4r \u00F6ppen.(iii) F\u00F6r varje \u00F6ppen delm\u00E4ngd \u00E4r en isomorfi. (H\u00E4r \u00E4r k baskroppen.)"@sv . . . . . . . "39544418"^^ . . . . "Inom algebraisk geometri, en del av matematiken, \u00E4r ett geometriskt kvot av en algebraisk varietet X med verkan av en G en s\u00E5 att (i) F\u00F6r varje y i Y \u00E4r fibern en bana av G.(ii) Topologin av Y \u00E4r : en delm\u00E4ngd \u00E4r \u00F6ppen om och bara om \u00E4r \u00F6ppen.(iii) F\u00F6r varje \u00F6ppen delm\u00E4ngd \u00E4r en isomorfi. (H\u00E4r \u00E4r k baskroppen.)"@sv . . . . . "2275"^^ . . "1072026337"^^ . . . "In algebraic geometry, a geometric quotient of an algebraic variety X with the action of an algebraic group G is a morphism of varieties such that (i) For each y in Y, the fiber is an orbit of G.(ii) The topology of Y is the quotient topology: a subset is open if and only if is open.(iii) For any open subset , is an isomorphism. (Here, k is the base field.)"@en . . "Geometric quotient"@en . . . . . "Geometriskt kvot"@sv . .