geometrically irreducible scheme

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• Irreducible component — In mathematics, the concept of irreducible component is used to make formal the idea that a set such as defined by the equation: XY = 0is the union of the two lines: X = 0and : Y = 0.The notion of irreducibility is stronger than connectedness.… …   Wikipedia

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• Homogeneous coordinate ring — In algebraic geometry, the homogeneous coordinate ring R of an algebraic variety V given as a subvariety of projective space of a given dimension N is by definition the quotient ring R = K[X0, X1, X2, ..., XN]/I where I is the homogeneous ideal… …   Wikipedia