Algebraic curves by Fulton W. PDF

Algebraic Geometry

By Fulton W.

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Let qi denote the row vectors of the transpose of Φ. That is, qi represents the multi-grading of the homogeneous coordinate xi . Let TV be the tangent sheaf of V . Assuming V is smooth, we have the generalization of the Euler exact sequence for a toric variety [12] (4) / O ⊕r 0 xi qi V / N −1 / TV OV (qi ) / 0. i=0 Let N −1 (5) qi . Q= i=0 For the complete intersection X we have the adjunction exact sequence: (6) / TX 0 / TV |X / OX (Qa ) a / 0, where Qa is the multi-degree of the equation f a .

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