Algebraic Geometry
《Algebraic Geometry》 · 第 429 页 · Appendix A，Section 3，Definition
Let $\mathcal E$ be a locally free sheaf of rank $r$ on a nonsingular quasi-projective variety $X$. For each $i=0,1,\ldots,r$, we define the $i$th Chern class $c_i(\mathcal E)\in A^i(X)$ by the requirement $c_0(\mathcal E)=1$ and $\sum_{i=0}^r(-1)^i\pi^*c_i(\mathcal E)\cdot\xi^{r-i}=0$ in $A^r(P(\mathcal E))$, using the notation of (A11).