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The point is that the class ξ depends on the vector bundle you choose, so in your two presentations the two ξ 's are not the same thing. In fact ξ.

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The class ϕ n − 1 has degree 1 when restricted to each fibre of f since H n − 1 has degree 1 on P n − 1, where H is the class of a hyperplane.

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stick to smooth complex projective varieties because these are our main CH∗( X) (respectively CH∗(X)) for the Chow group (respectively, the Chow ring) . bundles E on X, we know that ci(E) is a smooth cycle, for any i ≥ 0.

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Transversality and the Chow ring. Some techniques for computing the Chow ring 22 .. Chapter 9 Projective bundles and their Chow rings

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The Chow ring of the flag variety has a natural basis given by the Schubert cycles . The central . We rather stick to the former than to the . We will also use repeatedly the projective bundle formula, which can be found e. g. in [14,. Section ].

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the push-forward morphism for certain Chow rings ([10], Theorem , see also Section We rather stick to the former than to the latter. . E! X a vector bundle of rank two on X. Consider the projective line fibration Y ¼ PрEЮ.