Remark 42.37.3. We could also rewrite equation 42.37.1.1 as

42.37.3.1

\begin{equation} \label{chow-equation-signs} \sum \nolimits _{i = 0}^ r c_1(\mathcal{O}_ P(-1))^ i \cap \pi ^*c_{r - i} = 0. \end{equation}

but we find it easier to work with the tautological quotient sheaf $\mathcal{O}_ P(1)$ instead of its dual.

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