Lemma 82.30.1. In Situation 82.2.1 let X/B be good. Let \mathcal{E}, \mathcal{F} be finite locally free sheaves on X of ranks r, r - 1 which fit into a short exact sequence
0 \to \mathcal{O}_ X \to \mathcal{E} \to \mathcal{F} \to 0
Then we have
c_ r(\mathcal{E}) = 0, \quad c_ j(\mathcal{E}) = c_ j(\mathcal{F}), \quad j = 0, \ldots , r - 1
in A^*(X).
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