A remark on the Chern class of a tensor product

Paolo Aluffi, Carel Faber

This ridiculously short note is devoted to the proof of the following fact: if \alpha is a class of rank r in the Grothendieck group of vector bundles over a scheme, and L is a line bundle, then c_{r+1}(\alpha) = c_{r+1}(\alpha\otimes [L]).

The proof is elementary. Maybe the most interesting thing about this is that it shows up with surprising frequence in intersection-theoretic computations inspired by enumerative geometry.